UNIVERSITY OF ILLINOIS BULLETIN 

Vol. XIX October 31, 1921 No. 9 

Issued Weekly 

[Entered as second-class matter December n, 1912, at the post office at Urbana, Illinois, under the 
Act of August 24, 1912. Acceptance for mailing at the special rate of postage provided for 
in section 1103, Act of October 3, 1917, authorized July 31, 1918.] 



BUREAU OrEDUCATIONAL RESEARCH— BULLETIN NO. 6 

THE ILLINOIS EXAMINATION 



BY CllZ-^qO^l 



Walter S. Monroe 

DIRECTOR 

BUREAU OF EDUCATIONAL RESEARCH 
COLLEGE OF EDUCATION, UNIVERSITY OF ILLINOIS 




PRICE 50 CENTS 



PUBLISHED BY THE UNIVERSITY OF ILLINOIS 
URBANA 



^l^onognpt 



THE ILLINOIS EXAMINATION 



BY 



Walter S. Monroe 

DIRECTOR 



Bureau of Educational Research 
College of Education, University of Illinois 




PUBLISHED BY THE UNIVERSITY OF ILLINOIS 
URBANA, ILLINOIS 



v^$^ 



TABLE OF CONTENTS 

PAGE 

Preface 4 

Introduction 5 

I. Facts of Title 6 

II. Nature of Pupil's Performance 6 

1. Illinois General Intelligence Scale 6 

2. Monroe's Standardized Reading Tests, Revised 10 

3. Monroe's General Survey Scale in Arithmetic 12 

III. Description of Pupil's Performance 17 

1. Point Scores 17 

2. Derived Scores 19 

IV. Function 43 

V. Validity 43 

1. Objectivity 43 

2. Reliability 43 

3. Discrimination 50 

Comparison with criterion measures 57 



Inferences concerning validity based upon the struc- 
ture of the test and its administration 59 



VI. Validity of Significance 61 

VII. Norms 65 



PREFACE. 

In this bulletin we present an account of the derivation of the battery 
of educational tests known as the Illinois Examination. In addition, we 
include data relative to their validity, reliability, practice effect, norms, 
and significance. Doubtless some readers will not find all of the infor- 
mation relative to these tests which they desire. Although an effort has 
been made to have the account complete the author himself is conscious 
of a number of limitations of this report. It is, however, presented in 
hopes that it will be of service to those who are interested in the Illinois 
Examination. 

On April 2, 1920, a "Committee on Standard Tests" of the Illinois 
Association of County Superintendents met in conference at the Univer- 
sity of Illinois, in order to decide upon a testing program for rural schools. 
A group of three tests, including one for the measurement of general in- 
telligence, one for measuring ability to read silently, and one for measur- 
ing abilities in the field of arithmetic, were recommended to the committee 
by the Bureau of Educational Research. Although the school year was 
far advanced it was decided to incorporate in this battery of tests, the 
achievement quotient which had been conceived in another connection. 

It is obvious that educational research of the type represented by the 
bulletin is possible only through the cooperation of a large number of 
persons. The writer is glad to acknowledge the cooperation oi^ first y the 
city superintendents and teachers who gave the preliminary form of the 
tests in May, 1920, second, the county superintendents and others who 
cooperated in the giving of the tests in October, 1920, and thirdy those city 
superintendents and teachers who gave portions of the Examination in 
the spring of 1921 in order to determine the reliability of the tests. Ac- 
knowledgement is made in the body of the bulletin for special contributions. 

WALTER S. MONROE, Director. 



THE ILLINOIS EXAMINATION, 

INTRODUCTION 

The Illinois Examination, published in the form of a sixteen page 
booklet, is the name given to a battery of tests: The Illinois General In- 
telligence Scale, Monroe's Standardized Silent Reading Tests, Revised, 
and Monroe's General Survey Scale in Arithmetic* However, the signi- 
ficant characteristic of the Illinois Examination is not that of merely put- 
ting these three tests together in one booklet. It is rather the way in 
which the measures of achievement are combined with the measure of 
intelligence to secure the Achievement Quotient (A. Q.) The usual pro- 
cedure of interpreting measures of achievement by reference to grade norms 
provides for no consideration of the general intelligence of the pupil; all 
pupils, bright, average, and dull are judged with reference to the same 
norms. The plan by which the measures of achievement and general in- 
telligence are combined in the Illinois Examination was conceived in an 
effort to provide a procedure by which a pupil's general intelligence or 
his capacity to learn would be considered in interpreting his achievement. 

Briefly, the plan consists of establishing for the achievement tests 
mental age norms which are used to supplement the usual grade norms. 
For each half year of mental age, as shown by the general intelligence scale 
used, the median achievement was determined. These medians are the 
mental age norms, which are used as a basis for translating the point 
scores into achievement ages. In arriving at the mental age norms, all 
pupils of a given mental age in grades III to VIII inclusive were grouped 
together without regard to the grade in which they were classified. Pro- 
vision is made for comparing a pupil's achievement score, (when expressed 
as an achievement age) with the norm corresponding to his mental age by 
dividing his achievement age by the standard score for his mental age.** 
This quotient is called the Achievement Quotient. The plan involves 
certain assumptions and approximations. These, as well as the validity 
and the reliability of the several tests incorporated in the Illinois Exami- 
nation, will be considered in detail on the following pages. 

In the construction of the tests crude methods were frequently em- 
ployed in preference to more refined ones because of their greater sim- 
plicity and the saving of time thus secured. For example, this was done 
in the construction of the duplicate forms of the tests in silent reading and 
arithmetic and in deriving the basis for translating the point scores into 
age scores. In the latter case a more refined procedure involving the use 



"These tests are published by the Public School Publishing Co., Bloomington, Illinois. 
**This "standard score" is numerically the same as a pupil's mental age. 



of the regression equation might have been used. The results obtained 
by the use of the crude methods have been verified by a critical study of 
the test. 

I. FACTS OF TITLE. 

In so far as the Illinois General Intelligence Scale represents original- 
ity, B. R. Buckingham is primarily responsible for it. Walter S. Mon- 
roe, the author of this bulletin, devised the two achievement tests, and 
also contributed the plan of combining measures of achievement with 
measures of intelligence. An experimental edition of the Illinois Exami- 
nation, including the scales for general intelligence and silent reading, 
was published in April, 1920. The complete examination together with 
the Teachers Handbook and class record sheet was first published during 
the summer of 1920 and was made available for distribution in August. 
The second form of the Illinois Examination was devised during the school- 
year of 1920-21 and was made available for use early in 1921. The 
Examination consists of two parts. Illinois Examination I is designed 
for grades III, IV and V. Illinois Examination II is designed for grades 
VI, VII, and VIII. The Illinois General Intelligence Scale is the same 
for all grades. The scales for reading and for arithmetic are diflFerent in 
the two examinations. There are two forms of the examination. A third 
form of the scales for silent reading and arithmetic has been prepared. 

II. NATURE OF PUPIl's PERFORMANCE. 

1. Illinois General Intelligence Scale. In the Illinois General In- 
telligence Scale the pupil is required to make a mark with his pencil or 
to write figures. No other writing is required of him. The marks consist 
either of a line drawn under a word or of a line crossing out a word or 
number. 

The scale consists of seven sub-tests which are illustrated by a few 
samples from each. 

Test No. 1— ANALOGIES 

1 eat — bread:: drink — water iron lead stones 1 

2 finger — hand::toe — box foot doll coat 1 

3 shoe — foot::hat — kitten head knife penny 3 

4 dress — women ::feathers — bird neck feet bill 4 

5 dog — puppy::cat — kitten dog tiger house 5 

The pupil is asked to draw a line under the word in heavy type re- 
lated to the third word as the second is related to the first. 



Test No. 2— ARITHMETIC PROBLEMS 

1 If one boy has 10 fingers, how many fingers have six boys? Answer ( ) 

2 There are 1 5 children in our class. 5 of them are boys. How many are 

girls? Answer ( ) 

3 We learn 2 words a day in our class. How many do we learn in 8 days? Answer ( ) 

4 Jack is 42 inches tall and Fred is 5 inches taller. How tall is Fred? . . . .Answer ( ) 

5 Mr. Gray sold ten bags of flour last Saturday at 2 dollars a bag. 

How many dollars did he get for the flour? Answer ( ) 

The pupil is required to write the answer within the parentheses. 
Test No. 3— SENTENCE VOCABULARY 

1 A gown is a string animal dress plant. 

2 Haste is hurry red little sweet. 

3 To tap is to run fall knock smile. 

4 A dungeon is open bright heavy dark. 

5 Majesty refers to dresses kings countries climates. 

The pupil is required to draw a line under that one of the last four 
words which makes a true sentence. 



Test No. 4— SUBSTITUTION 



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The pupil is to write in squares after the symbols the numbers to 
which they correspond as given by the key at the top. 

Test No. 5— VERBAL INGENUITY 

1 the cat at see. 

2 boy was sky the sick. 

3 Bread sweep will the kitchen I. 

4 are going yesterday to-morrow we. 

5 me mine give my straw hat. 



The pupil is to cross out the superfluous word. 
can then be made into a true sentence. 



The remaining words 



Test No. 6— ARITHMETICAL INGENUITY 

(1) 1 2 3 9 4 5 

(2) 2 4 6 7 8 

(3) 9 8 7 6 5 2 

(4) 11 10 8 6 4 2 

(5) 5 7 10 15 20 25 

The pupil is to cross out the number that does not fit in the group. 
Test No. 7— SYNONYM-ANTONYM 

1 high — low same — opposite 1 

2 go — leave same — opposite 2 

3 large — great same — opposite 3 

4 bitter— sweet same — opposite 4 

5 begin — commence same — opposite 5 

The pupil is required to indicate whether the first two words mean the 
same or the opposite by drawing a line under the word "same" or "oppo- 
site." 

These sub-tests were selected after analyzing a number of existing 
general intelligence scales with reference to sub-tests and after examining 
much that has been written on the topic of group intelligence scales. The 
opinion of certain experts in this field was also obtained. Test No. 1, 
Analogies, was made from exercises taken from the Army Scale Alpha. 
Test No. 2, Arithmetic Problems, was compiled from a collection of 
problems which Professor Buckingham had evaluated with reference to 
difficulty. Test No. 3, Sentence Vocabulary, is an abridgment of the 
Holley Sentence Vocabulary Scale. In general this abridgment was se- 
cured by taking every third exercise of the original test, beginning with the 
first. Test No. 4, Substitution, was contributed by Professor E. H. 
Cameron of the College of Education, University of Illinois. Test No. 
5, Verbal Ingenuity, and Test No. 6, Arithmetical Ingenuity, were taken 
from the Pressey Cross Out Tests.* Test No. 7, Synonym-Antonym, 
consists of exercises selected largely from the Army Scale Alpha. 

These seven sub-tests together with two others were given to a limited 
number of pupils before the preliminary edition was printed. On the 
basis of these data two of the sub-tests were eliminated and minor changes 
made in the seven retained. In general the exercises in each of the sub- 
tests are arranged in order of gradually increasing difficulty. 



•Acknowledgment is hereby made to Professor S. L. Pressey, of Ohio State University, 
for permission to use these tests. 



8 



Form 2 of the sub-tests was devised in either of two ways. The first 
method was to make use of "standardized exercises," either in the files of 
the Bureau of Educational Research, or available in published reports.* 
The second method involved the modification of the exercises of the first 
form in such a way as to change their identity with the least probable 
change in difficulty. 

The first method was used in the case of Test 1, Analogies; Test 2, 
Arithmetic Problems; Test 3, Sentence Vocabulary; and Test 7, Synonym- 
Antonym. For Test 1, exercises published by Professor R. Pintner in the 
Journal of Applied Psychology, June-September, 1920, were used. For 
Test 2, exercises were taken from Professor Buckingham's own list of such 
material. The exercises for Test 3 were taken from a list of such exercises 
evaluated by Dr. C. E. Holley when he was engaged in the derivation of 
his Sentence Vocabulary Scale. The exercises for Test 7 were taken from 
the Army Scale Alpha as was done in the case of Form 1. 

Form 2 of Test 4, Substitution, was constructed by using the same 
characters as in Form 1, but changing their numerical equivalents. The 
second form of Test 5, Verbal Ingenuity, and of Test 6, Arithmetical In- 
genuity, are merely modifications of Form 1. Several modifications of 
each of the exercises were given to pupils and that one selected which proved 
to be most nearly of the same difficulty as the corresponding exercise of 
Form 1. 

The pupil is made acquainted with the nature of the exercises in each 
sub-test by means of a few sample exercises in addition to a verbal explana- 
tion. With the exception of Test 2, Arithmetic Problems, three or four 
sample exercises are given for each sub-test. The time allowance for each 
of the sub-tests is given below. In each case it is intended that no pupils, 
€ven the brightest, will finish all of the exercises within the time allowed. 
Test 1, Analogies, 2 minutes 

Test 2, Arithmetic Problems, 3 

Test 3, Sentence Vocabulary, 2 

Test 4, Substitution, 3 

Test 5, Verbal Ingenuity, 3 

Test 6, Arithmetical Ingenuity, 2 

Test 7, Synonym-Antonym, 1 

Total 16 minutes 

Equivalence of duplicate forms. In order to determine the degree of 
equivalence of the two forms of the Illinois General Intelligence Scale, 
copies of the two forms were arranged in alternate order and distributed to 



*This standardization refers to the determination of the difficulty of the exercises upon 
the basis of the percent of pupils who were able to do them correctly. 



pupils as they happened to be seated. This was done in a number of school 
systems. The median and average scores secured from the two forms in 
this way are given in Table I. The median and average scores are ex- 
pressed in terms of points. The differences for both the median and the 
average show that the forms are approximately equal. These differences 
vary slightly from grade to grade. The greatest difference exists in the 
fourth grade. Except in two instances the differences are positive which 
shows that the second form yields slightly larger scores than the first. 
This means that the second form is slightly easier than the first. When the 
six grades are combined the difference between the medians is 0.8. The 
difference of the averages is 2.3. Since, as we show later, 10.0 points of a 
pupil's score are equivalent to one year of mental age, we may say that in 
general the non-equivalence of the two forms of this scale is probably not 
more than two months. 

TABLE I. DEGREE OF EQUIVALENCE OF FORMS I AND 2 OF ILLINOIS GENERAL 
INTELLIGENCE SCALE 





No. of Pupils 


Median 


Score 


Differ- 
ence 


Average Score 


Differ- 
ence 


Grade 
































Form 


Form 


Form 


Form 


Form 2- 


Form 1 


Form 2 


Form 2- 




1 


2 


1 


2 


Form 1 






Form 1 


III 


331 


325 


32.3 


32.7 


0.4 


33.1 


33.7 


0.6 


IV 


298 


295 


46.0 


50.5 


4.5 


47.3 


51.5 


4.2 


V 


336 


334 


56.9 


56.7 


-.2 


58.0 


59.4 


1.4 


VI 


300 


288 


73.7 


76.2 


2.5 


75.1 


76.0 


0.9 


VII 


289 


279 


81.9 


84.1 


2.2 


82.6 


83.8 


1.2 


VIII 


240 


253 


102.1 


101.3 


-.8 


101.3 


102.7 


1.4 


III-VIII 


1794 


1774 


62.5 


63.3 


0.8 


63.8 


66.1 


2.3 



2. Monroe's Standardized Silent Reading Tests, Revised. In these 
tests the pupil is asked to read a series of exercises which have no con- 
nection with each other. In each exercise the pupil is required to read a 
paragraph and to answer a question based upon it. The answer is to be 
given by drawing a line under a word or by indicating it in some other 
way. No writing is required. In most exercises the pupil has to select 
one out of five words in making his response; in a few there are only four 
words. The nature of the exercises may be illustrated by the following. 
The first two are taken from Test I and the others from Test II: 



10 



It was a rainy, dark, dismal day. The children had not been allowed to go out to play 
all day. Their lessons were poor and the teacher cross. It was late in the afternoon. 
Draw a line under the word that tells how the children felt. 
active smiling happy cross good 
"The golden rod is yellow, 

The corn is turning brown, 
The trees in apple orchards 
With fruit are bending down." 
Draw a line under the season of the year you think is pictured in this stanza. 

autumn spring winter summer 
It was cold, bleak, biting weather; foggy withal; and he could hear the people in the 
court outside go wheezing up and down, beating their hands upon their breasts and stamping 
their feet upon the pavement-stones to warm them. 

What kind of picture does this paragraph describe? 

comfortable luxurious cheerless pleasant exciting 
The caravan, stretched out upon the desert, was very picturesque; in motion, however, 
it was like a lazy serpent. By and by its stubborn dragging became intolerably irksome to 
Balthasar, patient as he was. 

Place a line under the word which tells in what respect the caravan resembled a serpent. 

temper color length motion size 
In front the purple mountains were rising up, a distant wall. Cool snow gleamed upon 
the summits. Our horses suffered bitterly for water. Five hours we had ridden through 
all that arid waste without a pause. 

What kind of a country had these people been riding through? 

mountainous swampy desert forest valley 

The exercises for Form 1 were taken with some modifications from the 
original edition of Monroe's Standardized Silent Reading Tests. In 
selecting the exercises, and in making the modifications, an effort was made 
to have all the exercises approximately the same length. Those for test 
II are slightly longer than the ones included in Test I. The exercises are 
not absolutely equal with respect to difficulty. They are arranged so that 
in general there is a slight increase in difficulty from exercise to exercise 
but in no sense can they be considered a difficulty scale. To secure ab- 
solute uniformity with respect to difficulty would have required the ex- 
penditure of a prohibitive amount of labor. Even if this were not true it 
is believed to be desirable to have a moderate range of difficulty in view of 
the fact that the exercises are to be given to pupils in a sequence of three 
successive school grades. 

The nature of the exercises is explained to the pupils by means of 
three fore-exercises. In addition they are given certain verbal explana- 
tions. Four minutes are allowed for the test in all grades. This time al- 
lowance was intended to be such that practically no pupils would complete 
the tests; but it has been found that this is not always the case. 



II 



A few of the exercises are based on poetry although the majority are 
based on prose paragraphs. In light of a recent investigation* it appears 
likely that the reading of poetry, even for the purpose of answering a ques- 
tion, is not the same activity as the reading of prose for the same purpose. 
To the extent that this is true the test is not consistent, and this consti- 
tutes one of its limitations. In a number of other respects a high degree 
of uniformity has been secured. In every case the pupil's response is the 
same. The exercises are approximately equal in length and the questions 
asked appear to call for much the same type of reading. 

Equivalence of duplicate forms. The three forms of each of the silent 
reading tests were arranged in alternate order and given in this order to 
pupils as they were seated in a number of cities. Table II gives the median 
and average comprehension scores for each of the three forms.** With 
few exceptions these differences are less than one. A few are negative 
but most are positive. In the case of Test I, when the scores from grades 
III to V inclusive are combined, the three forms are shown to be very 
nearly equivalent both by the difference of the medians and by the differ- 
ence of the averages. In the case of Test II, which is designed for grades 
VI, VII, and VIII, Forms 1 and 2 are shown to be exactly equivalent by 
the medians and approximately so by the averages. Form 3, however, 
appears to be slightly easier, thus yielding slightly larger scores than 
either Form 1 or Form 2. The difference approaches a year of achieve- 
ment in comprehension.*** 

In Table III, corresponding data are given for the rate scores. The**** 
differences here are larger. This is partly due to the fact that rate scores 
are expressed in terms of a much smaller unit than comprehension 
scores, but in this test the reading rate appears to be more erratic than 
comprehension. Although some of the differences for Test I are relatively 
small, corrections should be made when comparisons are made between 
scores obtained from the different forms. 

3. Monroe's General Survey Scale in Arithmetic. Scale I, designed 
for grades III, IV, and V, consists of eight sub-tests. Scale II, designed 
for grades VI, VII, and VIII, consists of seven sub-tests. In each sub- 
test, except No. 7, Scale II, the pupil is asked to do arithmetical examples. 
In Test 7, he is asked to insert the decimal point in quotients. 

*Pressey, L. W. and Pressey, S. L. "A critical study of the concept of silent reading 
ability." 'Journal of Educational Psychology, 12:25-31, January, 1921. 

**The unit in terms of which scores are expressed is relatively large. It approaches one 
year of achievement in comprehension of silent reading. 

***Since Form 3 is not incorporated in the Illinois Examination, its non-equivalence 
with the other two forms does not constitute a limitation of this battery of tests. 

****Except for the lower achievement ages, 7 or 8 units are equivalent to one year 
of achievement in rate of silent reading. 

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In selecting the sub-tests for each scale, an effort was made to include 
examples of the types most appropriate for the pupils to whom they would 
be given. Tests 1, 2, 3, and 4 of Scale I are on the fundamental combi- 
nations, or tables, one test being devoted to each operation. These tests 
are similar to the corresponding tests of the Courtis Standard Research 
Tests, Series A, and of the Cleveland Survey Tests. Test 5 calls for 
single column addition of five figures. Test 6 consists of subtraction 
examples, in which the subtrahend is a single figure. Test 7, multipli- 
cation, consists of multiplication examples in which the multiplier is a 
single figure. In Test 8, division, the divisor is a single figure. 

The sub-tests of Scale II are represented by the following samples: 
Test No. 1— ADDITION 

7862 6809 8941 5917 6772 7864 1249 

5013 7623 7910 4814 6028 7883 8975 

1761 5299 9845 9007 6535 8240 9005 

5872 6601 8522 6975 2340 9869 1573 

3739 3496 1046 1227 2319 6794 3203 





Test No. 2— MULTIPLICATION 






4857 




5718 6942 




4065 


36 




92 58 

Test No. 3— DIVISION 




47 


41)574 




79)36893 32)384 




58)27608 




Test No. 4— SUBTRACTION 






739 


1852 


975 1087 


516 


962 


367 


948 


906 821 


239 


325 



Test No. 5— ADDITION AND SUBTRACTION OF FRACTIONS 

11 3 2 13 

6 3 4 5 6 5 

Test No. 6— MULTIPLICATION AND DIVISION OF FRACTIONS 

2 3 4 2 5 3 

3 4 7 ■ 3 12 5 ~ 

Test No. 7— DECIMAL FRACTIONS 

.03)16.2 Ans. :54 .07)1.82 Ans.:26 .05).415 Ans.: 83 

.06)7.44 Ans.: 124 .08).952 Ans.: 119 .04)87.6 Ans.: 219 

.02).144 Ans.: 72 .08)40.8 Ans.: 51 .09)3.42 Ans.: 38 

IS 



Several of the sub-tests were taken bodily from Monroe's Diagnostic 
Tests in Arithmetic, Others were constructed similar to well known tests. 
In constructing the duplicate forms of these tests the figures of the ex- 
amples were rearranged or changed, so that examples identical in gross 
structure but leading to different answers were obtained. In the case of 
Scale I, Tests 1, 2, 3, and 4 were constructed by securing at random num- 
bers of the same general magnitude as those used in Form 1. In doing 
this, especially in Tests 1 and 3, many of the examples were repeated either 
in their identical form or with the position of the two numbers reversed. 
Test 5 was constructed by rearranging the same numbers actually used in 
Test 5 of Form 1. This rearrangement was largely, although not entirely 
so, a process of shifting the position of the example and reversing the order 
of numbers therein. In Test 6, two methods were used, either the sub- 
trahend and minuend were grouped together differently or the figures in 
the minuend were reversed. In Test 7, the figures in the multiplicand 
were rearranged and the resultant number grouped with another multi- 
plier. In Test 8, the same divisors were kept and the dividends either 
slightly increased or decreased so as to leave the quotients still integral 
numbers. 

In Test 1 of Scale II, the columns of figures in each example were 
shifted with occasional changes to prevent a zero from coming first in any 
number. In Test 2, the figures of the multiplicand were rearranged and 
the resultant number grouped with another multiplier. In Test 3, either 
the dividends were slightly increased or decreased so as to be evenly di- 
visible by the same divisor, or the dividend or divisor was multiplied or 
divided by two. In Test 4, either the figures of the minuend were arranged 
differently or new minuends were constructed by grouping together part 
of the figures from two minuends to form one, the remaining figures to 
form another. The subtrahends were either changed by a different ar- 
rangement of figures or by adding or subtracting a small number, such as 
ten or twenty, or they were not changed at all. Tests 5 and 6 were con- 
structed by a random selection of fractions of the same general magnitude 
as those of the same test in Form 1. In Test 7, the position of the decimal 
point in either divisor or dividend or in both was shifted, and the position 
of the examples was also changed. 

In almost all of the tests an occasional change, not covered by the state- 
ments above, was made, either because of the necessity of avoiding im- 
possible combinations or because the result by following too closely the 
procedure laid down seemed undesirable. 

Equivalence of Duplicate Forms. A study was made of the equiva- 
lence of the duplicate forms of Monroe's General Survey Scale in Arithme- 

i6 



tic in the same way that the equivalence of the duplicate forms of tests for 
general intelligence and silent reading was investigated. The results are 
given in Table IV, Since Forms 2 and 3 were constructed from Form 1 
by a rather mechanical procedure one might expect to find a higher degree 
of equivalence for the arithmetic scale than for the others. This, especially 
in the upper grades, is not true. In the case of Scale I, however, the 
differences are relatively small, particularly as shown by the averages.* 
In the case of Scale II the differences between Form 1 and Form 2 are 
small. Hence, these two forms may be considered as being very approxi- 
mately equivalent. Form 3 appears to be considerably easier than the 
other two. 

III. DESCRIPTION OF PUPIl's PERFORMANCE. 

Point Scores. The performance of a pupil upon each of the sub- 
tests of the Illinois General Intelligence Scale is described in terms of a 
point score. With two exceptions this point score is the number of exer- 
cises which he has done correctly in the time allowed. In order to give 
appropriate weight to Test No. 4, Substitution, the number of figures 
written correctly is divided by four. Since the possible score on this test 
is 150, as compared with 16 to 40 in the cases of the other tests, failure to 
weight the score from this test would give it an exceedingly high degree of 
potency in determining the pupil's total score. The rule to divide this 
score by 4 is purely arbitrary. In Test No. 7, Synonym-Antonym, in 
order to discount for the correct answers which might be obtained by 
merely giiessing, the pupil's score is given as the number of exercises right 
minus the number wrong; exercises skipped are counted as wrong; exer- 
cises not reached when time is called are not counted. The pupil's total 
point score is the sum of his scores on the seven sub-tests. 

In the case of Monroe's Standardized Silent Reading Tests, Revised, 
the pupil receives two scores. His comprehension score is the number of 
exercises which he answers correctly. His rate score is the number of 
words which he reads per minute or the total number of words read di- 
vided by 4, In order to obtain this rate the pupil is asked to mark the 
line which he is reading when the signal to stop is given. The cumulative 
totals of the words are printed in the left hand margin so that the total 
number of words read is easily obtained. 

The number of examples right is taken as the pupil's point score on 
each of the sub-tests of Monroe's General Survey Scale in Arithmetic. 
These sub-tests yield scores which differ widely in magnitude. Arbitrary 



*The equivalence of one year of achievement is 8 units of the point score. 

17 



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rules were adopted for weighting these scores so that approximately equal 
weight would be given to each test. (For details see the tests.) The 
weighted sum of the scores on the several sub-tests is the pupil's point 
score. 

Correction of scores derived from the scales designed for grades 
VI, VII, and VIII. In the cases of both silent reading and arithmetic, 
the tests for grades III, IV, and V are entirely different from those given in 
grades VI, VII, and VIII. This makes the scores from the two sequences 
of grades incomparable. They have a different zero point and it is not 
unreasonable to expect that they would be expressed in terms of a different 
unit. It is relatively easy to estimate the approximate difference between 
the zero points. This difference can be used as a correction to be added to 
the point scores obtained from the tests for the upper sequence of grades. 
This was done and it appears that the differences in the units are not 
sufficiently large to introduce serious inaccuracies when the corrected 
scores are considered comparable. 

The method of estimating the difference between the zero points may 
be illustrated by the case of silent reading. The medians of the point 
scores without correction were calculated for each grade. These were then 
represented graphically as shown in Figure 1. The curve of progress for 
grades III, IV, and V was then extended so that the extension would parallel 
the curve of progress for grades VI, VII, and VIII. This extension to- 
gether with the progress curve for the lower sequence of grades forms a 
progress curve for grades III to VIII inclusive. The distance between the 
extension and the original curve is assumed to represent the difference in 
the zero points of the two tests. 

The estimated corrections based upon the scores derived from the 
preliminary tests in May, 1920, for Monroe's Standardized Silent Reading 
Test II, Revised, were rate 17 and comprehension 4. The arithmetic 
tests were not given at this time but, on the basis of scores derived from 
similar tests, a correction of 16 was estimated as the proper amount to 
add to the point scores derived from Scale II. The scores derived from 
giving the Illinois Examination to fifty thousand children during the fall of 
1920 indicated that these estimates were incorrect. The revised estimates 
are: reading rate 29, reading comprehension 5, and arithmetic 22. When 
these corrections are added to the point scores derived from the corres- 
ponding tests in Examination II, the scores will, in general, be approxi- 
mately comparable to the corresponding scores derived from Examination 
I. 

2. Derived scores. The point scores yielded by the scales of the 
Illinois Examination are translated into age scores. From these quotients 

19 



»"2I READING COMPREHENSION 

SCOK& 

14 r 



READING RATE 




"2 21 211 3211 lEL 32 2 3ZI 

GRADE GRADE 

FIGURE 1. SHOWING METHOD OF ESTIMATING CORRECTIONS TO BE 
ADDED TO SCORES OF SCALE II. 

are calculated. The portion of the Illinois Examination devoted to the 
measurement of general intelligence and ability in silent reading was given 
to over seventy-five hundred pupils in May, 1920, for the purpose of 
standardization and of determination of the basis for calculating certain 
derived scores. When the complete examination was used in October, 
1920, the scores obtained indicated that the results secured in May in- 
volved a sufficiently large error to make necessary a re-determination of 
the grade norms and of the basis for calculating the derived scores. Un- 
fortunately, the data collected from the October testing were in such form 
that the determination of the basis for calculating the derived scores could 
not be worked out by direct methods. It was, therefore, necessary to use 
estimates instead of actual determinations, but these estimates have 
been verified whenever possible and appear to be approximately correct. 
Data, in the form required for the direct calculation of the basis for 
obtaining the derived scores, are available from the public schools o. 



20 



Decatur, Illinois, and from eight elementary schools of the city of Chicago. 
These data, particularly those from Decatur, do not appear to be entirely 
representative. However, it has seemed wise to describe the method 
in terms of the scores from these two cities. The estimates will be found 
to agree, in some instances, with the data collected in these two cities, but 
in others agreement will be lacking. 

The chronological age norms for the Illinois General Intelligence 
Scale are used as a basis for translating the point scores into mental age 
scores. In determining the age norms the distribution of point scores 
was secured for each half year of chronological age. For example, the 
point scores of all pupils whose chronological ages fell between nine years, 
and nine years and six months, were brought together in a distribution. 
The median of this distribution was taken as the age norm for this 
chronological age group. In Table V, the median point scores for each of 
the age groups are given for both Decatur and Chicago. In the second 
column of the table the average chronological age of the group is given. 
It will be noted that except for the extreme ages the median point scores 
tend to become larger as the pupils become older. 

This scale was given only to the pupils in grades III to VIII inclusive. 
If a pupil enters school at six years we may expect to find him in the third 
grade at eight years of age. Of course, if the pupil fails of promotion, he 
will not reach the third grade until he is older. Pupils younger than 
eight years attaining the third grade either have entered school before 
they were six or have skipped a grade. In this case the pupils are probably 
bright. The same thing is true to a somewhat less degree for the pupils 
whose ages fall in the 8.0-8.4 interval, and even in the interval from 8.5- 
8.9 there is some selection of the brighter pupils. All pupils eight years of 
age have not advanced to the third grade. Some of them have failed of 
promotion and are found in the first or second grade. In general, they are 
the duller pupils. Consequently, we may say that the age groups below 
nine years are selected so that they do not include all pupils whose ages 
fall within the groups. The less capable have been left out. In Chicago, 
the Illinois General Intelligence Scale was not given to III-B pupils. For 
this reason, the selection extends above nine years. 

A pupil who entered school at six years of age and was promoted each 
year would be found at fourteen in the ninth grade or first year of the 
high school. Furthermore, when pupils reach the age of fourteen, the 
compulsory attendance law does not apply with the same force as in the 
case of younger pupils. For these reasons the age-groups at the top of 
the table are selected. In general, they include pupils who have failed 
of promotion one or more times because they were not able to do the work 

21 



of the school satisfactorily. Hence, we should expect to find the median 
point scores for such pupils less than those for younger groups of unselected 
pupils. 

TABLE V. MEDIAN POINT SCORES OF CHRONOLOGICAL AGE GROUPS FOR 
DECATUR AND FOR EIGHT ELEMENTARY SCHOOLS IN CHICAGO 





Average 


Decatur 


Chicago 


Chronological 


Chronolog- 


















Age Interval 


ical Age 


No. of Pu- 


Median 


No. of Pu- 


Median 


o 




pils 


Point 
Score 


pils 


Point 
Score 


17.5-17.9 


17.75 


1 


40.0 






17.0-17.4 


17.25 










16.5-16.9 


16.75 


2 


54.5 


5 


57.5 


16.0-16.4 


16.25 


9 


70.0 


11 


61.7 


15.5-15.9 


15.75 


26 


64.5 


37 


67.9 


15.0-15.4 


15.25 


61 


64.4 


78 


75.3 


14.5-14.9 


14.75 


124 


71.4 


130 


72.4 


14.0-14.4 


14.25 


191 


68.9 


284 


70.0 


13.5-13.9 


13.75 


244 


73.5 


366 


67.6 


13.0-13.4 


13.25 


297 


70.2 


408 


72.2 


12.5-12.9 


12.75 


306 


67.2 


326 


67.1 


12.0-12.4 


12.25 


304 


63.4 


354 


63.1 


11.5-11.9 


11.75 


308 


52.8 


294 


57.8 


11.0-11.4 


11.25 


298 


54.8 


328 


55.2 


10.5-10.9 


10.75 


316 


43.8 


244 


46.9 


10.0-10.4 


10.25 


290 


40.9 


313 


48.0 


9.5-9.9 


9.75 


297 


35.9 


205 


44.4 


9.0-9.4 


9.25 


285 


30.1 


168 


43.2 


8.5-8.9 


8.75 


216 


26.2 


78 


40.0 


8.0-8.4 


8.25 


163 


20.0 


24 


38.3 


7.5-7.9 


7.75 


33 


27.5 


3 


42.5 


7.0-7.4 


7.25 


14 


23.0 






6.5-6.9 


6.75 


o 


20.0 







In Figure 2, the median point scores given in Table V are represented 
graphically. The Decatur scores are represented by small crosses and the 
Chicago scores by small circles. With the exception of the scores for the 
older pupils there is a suggestion of a straight line relationship between 
the point scores and chronological age. Other considerations, some of 
which will be mentioned later, led to the adoption of a straight line as 
representing the relation between the median point scores and the chronol- 
ogical ages. This line has been drawn in the figure. It is considered to 
extend indefinitely upward. It is extended downward until it cuts the 
vertical axis. This straight-line relationship permits the formulation of a 
very simple rule for translating point scores into mental ages. 

22 




o 



o 

» X 



1 1 1 I I L 



e a 10 i2 

CHRONOLOGICAL AGE 



16 



FIGURE 2. RELATION BETWEEN MEDIAN POINT SCORES AND CHRONOLOGI- 
CAL AGE. DECATUR MEDIAN SCORES REPRESENTED BY CROSSES AND 
CHICAGO MEDIAN SCORES BY SMALL CIRCLES. 

With reference to the extension of the Hne of relationship upward, 
it appears that the development of general intelligence, like physical de- 
velopment, does not continue indefinitely. The evidence at hand indi- 



23 



cates that beginning about 14 years there is a slowing down of develop- 
ment and that at about the age of 16 or 18 it ceases altogether* After 
this age, mental changes consist primarily in increasing the scope and 
skillfulness of the application of intelligence which one already possesses. 
An extension of the line of relationship which might be judged to conform 
with the actual median point scores for the higher age groups (assuming 
that all pupils belonging to these age groups were tested) would be curved 
downward and would tend to become horizontal or nearly so. This pro- 
cedure, which is the one followed in the Binet Scale and in a number of 
others, would not give us a method for translating the point scores made 
by the bright children in the upper grades into the corresponding ages. 
For example, a few pupils have made point scores as high as 185 on the 
Illinois General Intelligence Scale. On the basis of the facts at hand it is 
impossible to conceive that the median point score for any age group 
could possibly equal this. Therefore, if such point scores are to be trans- 
lated into mental ages it is necessary to devise another plan. The plan 
adopted was to extend the straight line of relationship upward until 
maximum point scores were reached. This plan has the merit of sim- 
plicity. 

If the downward extension of the line of relationship is examined it 
will be found that the point score which is equivalent to zero mental age 
is -55. This means that the absolute zero of the Illinois General Intelli- 
gence Scale is -55 points. Therefore, in translating point scores into cor- 
responding mental ages, it is necessary to correct this by adding 55 to the 
point score. When the slope of the line of relationship is examined it 
will be noted that the rise is approximately 10 points for one year of 
chronological age, which means that 10 points on the intelligence scale is 
considered equivalent to one year of mental age. Hence, we are able to 
state the rule, "Add 55 to the total point score and divide by 10. The 
quotient is the corresponding mental age." This rule is not absolutely 
accurate but it does not appear to involve errors greater than the errors 
of measurement which will be discussed in a later section. 

The validity of the rule for determining the mental ages was verified 
by comparing the results obtained by using it with the mental ages as de- 
termined by the Stanford Revision of the Binet Scale for Measuring In- 
telligence. Table VI gives the determinations of mental age by the two 
scales for 201 pupils.** Because of the small number of pupils in some 

*Children probably differ with reference to the development of their general intelligence. 
This slowing down probably begins at different ages in the cases of different pupils. Thus 
this statement should be interpreted as representing the average or typical development. 

**A portion of these data was furnished the writer by Professor J. C. DeVoss, of the Kan- 
sas State Normal School, Emporia, Kansas. The remainder was contributed by Superin- 
tendent L. W. Keeler, Michigan City, Indiana. 

24 



groups it is to be expected that some of the differences in mental age would 
be relatively large. An examination of the differences given in the last 
column of the table reveals that only three out of twenty are greater than 
one year. Many of the differences are very small. This table indicates 
that the rule adopted for translating point scores into mental ages gives 
results agreeing, as closely as could be expected in view of the errors of 
measurement which occur in using both scales, with the results obtained 
by using the Stanford Revision of the Binet Scale for Measuring Intellig- 
ence. 

TABLE VI. COMPARISON OF MENTAL AGES OF lol PUPILS BY BINET SCALE 
AND BY ILLINOIS GENERAL INTELLIGENCE SCALE 





Binet Scale 


Illinois 


J Scale 


Difference 


Number 
of 












Mental Age 


Mental Age 


Med. Point 


Corresp'd'g 


in Mental 


Pupils 


Interval 


Average 


Score 


Menta Age 


Ages 


2 


17.5-17.9 
17.0-17.4 


17.75 
17.25 


125.0 


18.00 


-.25 


2 


16.5-16.9 


16.75 


115 


17.00 


-.25 


2 


16.0-16 4 


16.25 


130.0 


18.50 


-2.25 


8 


15 5-15.9 


15.75 


90.0 


14.50 


1.25 


6 


15.0-15 4 


15.25 


105 


16.00 


- 75 


5 


14.5-14.9 


14.75 


75.0 


13.00 


1 75 


9 


14.0-14.4 


14.25 


85.0 


14.00 


.25 


13 


13.5-13.9 


13.75 


92.1 


14.71 


-.96 


19 


13.0-13.4 


13.25 


78.8 


13.38 


-.13 


11 


12.5-12.9 


12.75 


71 7 


12.67 


.08 


11 


12.0-12.4 


12.25 


63.0 


11.80 


.45 


18 


11.5-11.9 


11 75 


64.0 


11.90 


-.15 


32 


11.0-11.4 


11.25 


58.8 


11.38 


-.13 


16 


10.5-10.9 


10.75 


57.5 


11.25 


-.50 


18 


10.0-10.4 


10.25 


44.0 


9.90 


.35 


10 


9.5-9.9 


9.75 


50.0 


10.50 


-.75 


8 


9.0-9.4 


9.25 


36.3 


9.13 


.12 


5 


8.5-8.9 


8.75 


28.3 


8.33 


.42 


3 


8.0-8.4 


8.25 


27.5 


8.25 


.00 


3 


7.5-7.9 


7.75 


25.0 


8.00 


-.25 



The original data* from which Table VI was obtained are represented 
graphically in Figure 3. The coordinates of each dot in this figure repre- 
sent the mental ages of a pupil as determined by the two scales. The 
abscissa represents mental age as determined by the Illinois Examination. 
The ordinate represents the mental age as determined by the Binet Scale. 
The two instruments yield approximately the same mental ages for a 



*Two additional cases are represented in the figure. 

25 



number of pupils. For others the difference is marked. It must be re- 
membered that neither of the instruments is perfect and that when a dif- 
ference exists between the two mental ages it is likely to be due to the fact 
that both rather than only the mental age yielded by the Illinois General 
Intelligence Scale involve errors. 

ILLINOIS GENERAL im-ELLIGENCE SCALE 

6S 65 lOS 12.5 14.5 16.5 \6.5 T 

— 1 I . I « I 1^ 

2 



17.5 
165 
15.5 
IAS 
13.5 
J25 
IJ.5 
10.5 
9.5 
63 
73 


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qji- 2.65 


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pL- 


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22 
30 
23 
48 
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13 



T I 3 17 16 26 27 29 26 Id 18 fO 3 5 2 203 

FIGURE 3. RELATION OF MENTAL AGES OF 203 PUPILS AS DETERMINED 
BY THE ILLINOIS GENERAL INTELLIGENCE SCALE AND BY THE BINET 
SCALE. 

It should be borne in mind that mental ages above 14 obtained by the 
Illinois General Intelligence Scale must be interpreted somewhat differ- 
ently from the mental ages obtained by other scales, especially the Stanford 
Revision of the Binet Scale. The extension of the concept of mental age 
which is here introduced is believed to be justified by the practical con- 
sideration of finding a convenient device to represent the absolute intelli- 
gence of bright children in the upper grades. 

The intelligence quotient (I. Q.) is a measure derived by dividing a 
pupil's mental age by his chronological age. More strictly speaking the 
I. Q. is the quotient of a pupil's mental age divided by the median mental 
age for his chronological age. Below the age of 14 these are identical. 
A pupil's I. Q. is an index of his intelligence. If it is 100 he possesses only 



26 



average intelligence; if it is greater than 100, he is brighter than the aver- 
age; if less than 100 he is duller. Because the mental ages above 14 do not 
have the same meaning as the corresponding mental ages obtained from 
the use of the Stanford Revision of the Binet Scale, it follows that the I. 
Q.'s for these ages also have a modified significance. For this reason 
reason Otis has called the quotient which we are using the "coefficient of 
brightness." Since below the age of 14 the quotient yielded by the Illi- 
nois General Intelligence Scale is identical in meaning with the quotient 
derived by the Stanford Revision of the Binet Scale, it has seemed wise to 
retain the name, intelligence quotient. 

To facilitate the calculation of the I. Q. a table has been prepared 
which gives the I. Q.'s for each half year. This is reproduced as Table 
VII. The quotients have been calculated with reference to the mid-point 
of the intervals. Thus the quotient for chronological age group, 12-6, 
and mental age, 16-0, was found by dividing 16.25 by 12.75. A slightly 
different procedure was followed for chronological ages between 14 and 
18. As noted above it is assumed that within this period there is a gradual 
slowing down of the growth of general intelligence. Hence, the diff^erences 
between the actual median point scores for successive chronological age 
groups will gradually decrease and become zero at 18. Although the in- 
telligence quotient is generally defined as the quotient obtained by di- 
viding a pupil's mental age by his chronological age it is essentially the 
quotient obtained by dividing his mental age by the mental age norm for 
his chronological age. Below the age of 14 the norm and the pupil's 
chronological age are numerically the same. Above the age of 14 they 
are different. The quotients in Table VII for the age of 14 and above were 
calculated by using the mental age norm instead of the chronological age 
as the divisor. 

The first column of the table contains point scores corresponding to 
the mental ages (M. A.'s) given in the second column. For example, a 
point score of 60 corresponds to a mental age of 11 years and six months, 
and a point score of 65 is equivalent to a mental age of 12 years. If a 
pupil's point score is 61, 62, 63, or 64, it is taken, when using this table, 
as meaning a mental age of 1 1 years and six months. Similarly, a pupil's 
chronological age is considered to be 10 years until it is 10 years and six 
months. 



27 



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28 



To find a pupil's I. Q. in this table proceed as follows: Take, for ex- 
ample, a pupil whose point score is 82 and whose chronological age is 11 
years and four months. Find the interval* in the first column of numbers 
which contains a point score of 82. This is the 80 interval and the cor- 
responding mental age (M. A.) is 13 years and 6 months. Locate at the 
top of the table the interval for a chronological age of 11 years; follow down 
the column for this interval to the line for the point score of 80. The 
number at the intersection of this column and this line is the pupil's I. Q. 
It is 122. If a pupil's chronological age is more than 18 years ^ call it 18. 
His I. Q. will always be found in the last column of the table. 

As we shall show later there is evidence that the intelligence quotients 
yielded by this test have a greater variability than those obtained from the 
Stanford Revision of the Binet Scale. Therefore, when interpreting the 
I. Q.'s derived from the Illinois General Intelligence Scale in terms of 
degrees of brightness, it will be necessary to use a basis different from that 
proposed by Terman and others. (See page 67). 

The distributions of the intelligence quotients furnish additional evi- 
dence of the validity of the rule for translating the point scores into mental 
ages. In Figure 4, the distribution of the I. Q.'s of the pupils of Decatur 
is represented graphically. In forming this distribution all grades have been 
combined, but the shape of the distributions for the separate half grades 
approximates that of this total distribution. The total number of pupils 
is 3787. The only conspicuous departure from the normal curve is in the 

PUPILS 

eoor 



600 



400 



200 



40 



60 



60 



K)0 



tzo 



lAO 



160 



FIGURE 4. DISTRIBUTION OF PUPILS ACCORDING TO THEIR INTELLI- 
GENC E QUOTIENTS. 

*The term "interval" is used to indicate a span of point scores or ages. For the intelli- 
gence scores the span is five scores and in the table only the lower limit of this interval or span 
is given. For ages the interval is six months, and again only the lower limit is given. 



29 



90-100 interval. This is due to the structure of the table used for calcu- 
lating I. Q.'s. Thus, we may say that the distributions of I. Q.'s do not 
indicate any error resulting from the rule used for translating point scores 
into mental ages. 

Derived scores for achievement tests. To facilitate the comparison 
of a pupil's achievement with his mental age which represents his capacity 
to learn, provision was made for translating the point scores derived from 
the tests on arithmetic and silent reading into achievement age scores. 
The method of arriving at the basis for making this translation is similar 
to that used in the case of an intelligence scale. The point scores derived 
from all grades were thrown together and a distribution of the achievement 
scores was secured for each mental age group.* Because the data collected 
in May, 1920, were not representative, it is again necessary to illustrate 
the procedure and then to give the estimates which are recommended for 
use. Table VIII gives the median achievement point scores for the mental 
age groups for the city of Decatur. In this table the interval of mental 



TABLE VIII. 


MEDIAN ACHIEVEMENT 


POINT SCORES FOR MENTAL AGE 






GROUPS IN DECATUR 






Mental 


Aver- 


Num- 


Arithmetic 


Silent Reading 
Comprehen- 


Silent Reading 
Rate 


Age 
Interval 


age 

Mental 


ber of 
Pupils 






sion 




















Age 




Median 
Point 
Score 


Correspond- 
ing Age 
Score 


Median 
Point 
Score 


Corres- 
ponding 
Age 
Score 


Median 
Point 
Score 


Corres- 
ponding 
Age 
Score 


18.0-18.9 


18.5 


13 


78.4 


16.3 


17.7 


18.2 


233.2 


21.2 


17.0-17.9 


17.5 


26 


57.6 


13.7 


15.5 


16.0 


206.0 


17.5 


16.0-16.9 


16.5 


62 


63.2 


14.4 


15.5 


16.0 


218.0 


19.0 


15.0-15.9 


15.5 


146 


62.4 


14.3 


14.4 


14.9 


202.8 


17.1 


14.0-14.9 


14.5 


211 


56.0 


13 5 


13.9 


14.4 


185.2 


14.9 


13.0-13.9 


13.5 


323 


53.2 


12.9 


13.0 


13.5 


170.0 


13.0 


12.0-12 9 


12.5 


432 


48.0 


12.5 


12 


13.0 


157.6 


11.8 


11.0-11.9 


11.5 


485 


40.8 


11.7 


10.0 


11.0 


148.0 


11.0 


10.0-10.9 


10.5 


481 


34.4 


10.8 


9.7 


10.7 


139.4 


10.4 


9.0-9.9 


9.5 


479 


24.0 


9.5 


8.2 


9.6 


124.0 


9.5 


8.0-8.9 


8.5 


487 


16.0 


8.6 


6 6 


8.8 


105.2 


8.7 


7.0-7.9 


7.5 


373 


10.0 


8.0 


4.4 


8.1 


88.0 


8.1 


6.0-6.9 


6.5 


251 


6.0 


7.6 


3.0 


7.5 


70.6 


7.6 


5.0-5.9 


5.5 


23 


5.0 


7.5 


.5 


6.9 


36.0 


6.9 



*Before doing this the achievement point scores derived from the scales designed for the 
upper sequence of grades were corrected by adding the numbers given on page 19. 

30 



age is one year.* There are 432 pupils whose mental ages fall between 
12 and 13 years. Their average mental age is 12.5. Their median point 
score on the arithmetic scale is 48.0. This corresponds to an achievement 
age of 12.5. That is, the median achievement of the pupils belonging to a 
mental age group is taken as the equivalent of the corresponding achieve- 
ment age. In comprehension of silent reading the median point score 
of these pupils was 12.0. This is taken as corresponding to the achieve- 
ment age of 13.0.** In rate of silent reading their median point score was 
157.6. This is taken as corresponding to an achievement age of 11.8. 
The lack of agreement between the achievement age in rate of silent 
reading and the average mental age of this group is due to the fact that this 
group has not made as high a score in rate of reading as pupils of this mental 
age normally do. It must be remembered that these tables are based upon 
the scores of one city only. In addition to the data secured from Decatur, 
it was possible to make use of the grade norms derived for the Illinois 
Examination from 49,500 scores. Table IX gives the median point 
scores and the median mental age for each grade. 

TABLE IX. GRADE NORMS FOR ILLINOIS EXAMINATION 









Silent 1 


^.eading 


Grade 


Median Men- 
tal Age 


Arithmetic 
















Comprehen- 


Rate 








sion 




III 


7.9 


10 


3.8 


82 


IV 


9.4 


21 


7.7 


122 


V 


10.7 


35 


9.8 


142 


VI 


12.0 


44 


11.0 


158 


VII 


13.1 


53 


12.1 


170 


VIII 


14.3 


60 


13.5 


183 



*A mental age interval of six months is preferable. It is not used in this illustration 
because the data were originally tabulated in yearly intervals for another purpose. 

**The achievement age scores corresponding to the comprehension point scores were ob- 
tained by means of Table X. The unit of the point score is relatively large. Therefore, 
precise statements of equivalence were not shown in this table because fractional point scores 
are never obtained for individual pupils. This accounts for some of the apparent irregulari- 
ties in the age scores for comprehension of silent reading. 



31 



In Figure 5, the median point scores derived from the arithmetic scale 
in Decatur are represented graphically by small crosses. The grade norms 
are represented by small circles. In arriving at the general relationship 
which exists between achievement and mental age it is necessary to bear 
in mind that the groups in the extremes of Table VIII are small and per- 
haps not representative. The pupils whose mental ages fall between 5 
and 6 years probably have not learned to read well. Since the intelligence 
scale requires that the pupil be able to read, these mental ages are probably 
lower than they should be. At the upper end of the table we, of course, 
have very bright pupils, and bright pupils are likely to make higher scores 
than average or dull pupils of the same age. In Figure 5, a line has been 
drawn which is judged to represent the relation between achievement 
in the operations of arithmetic and mental age. This line can be used as 
a means for translating point scores into achievement ages. No simple 
rule can be stated as in the case of the intelligence scale. The achieve- 
ment ages corresponding to the point scores yielded by the arithmetic 
scale are given in Table X. 
MA. 



\9 r 




\0 



ZO 



60 



70 



30 AO 50 

ARITHMETIC 
FIGURE 5, LINE OF RELATIONSHIP BETWEEN MEDIAN POINT SCORES IN 
ARITHMETIC AND MENTAL AGE. 

32 



TABLE X. CORRESPONDING ACHIEVEMENT AGE FOR POINT SCORES IN ARITH- 
METIC AND SILENT READING 




Point scores 


Achieve- 
ment Age 






Rate 


Compre- 
hension 


Arith- 
metic 






250 
247 
244 




140 
136 
132 


24-0 
23-6 
23-0 






241 

238 

235 




128 
124 
120 


22-6 
22-0 
21-6 






232 
229 
226 


20 


116 
112 
108 


21-0 
20-6 
20-0 






222 
218 
214 


19 
18 


104 

100 

96 


19-6 
19-0 
18-6 






210 
206 
202 


17 


92 
88 
84 


18-0 
17-6 
17-0 






198 
194 
190 


16 
15 


80 

76 
72 


16-6 
16-0 
15-6 






186 
182 
178 


14 


68 
64 
60 


15-0 
14-6 
14-0 






174 
170 
165 


13 
12 


56 

52 
48 


13-6 
13-0 
12-6 






160 

154 
148 


11 
10 


44 
40 
36 


12-0 
11-6 
11-0 






141 
133 
124 


9 
8 


32 
28 
24 


10-6 

10-0 

9-6 






113 
100 

85 


7 
6 

4 


20 
15 
10 


9-0 
8-6 
8-0 






67 

47 
25 


3 
1 



5 



7-6 
7-0 
6-6 













6-0 





33 



Figure 6 and Figure 7 represent corresponding data for comprehension 
and rate of silent reading. The point scores corresponding to the various 
achievement ages are also given in Table X. 

When measures of both achievement and general intelligence are ex- 
pressed in terms of ages they may be considered comparable. The Illi- 
nois Examination provides for comparison by dividing the pupil's achieve- 
ment age by his mental age.* The quotient is called his achievement 
quotient. (A. Q.) 




I I I 



O I 2 3 A 5 6 7 6 9 \0 U 12 13 14 15 16 17 18 

COMPREHENSION 

FIGURE 6. LINE OF RELATIONSHIP BETWEEN MEDIAN POINT SCORES IN 
COMPREHENSION OF SILENT READING AND MENTAL AGE. 



*The achievement age norm for a pupil is numerically the same as his mental age. Hence, 
this procedure may also be thought of as being a comparison of a pupil's achievement with the 
norm for his mental age. 



34 




40 



60 60 



\60 [60 ZOO 2Z0 



100 120 140 
RATE. 
FIGURE 7. LINE OF RELATIONSHIP BETWEEN MEDIAN POINT SCORES IN 
RATE OF SILENT READING AND MENTAL AGE. 



This is an index of the extent to which his achievement corresponds 
to his general intelligence or capacity to achieve. For example, if a pupil 
has an achievement age of 12 years and a mental age of 9 years, his ac- 
chievement quotient is 133, (The decimal point is omitted as in the case 
of intelHgence quotients.) If this pupil's mental age had been 14 years, 
his achievement quotient would have been 86. An achievement quotient 
of 100 means that the pupil has achieved exactly the average of pupils 
of his mental age, or that he is just up to the norm for his mental age. 
If his achievement quotient is 130, he has achieved thirty percent more 
than the average of the pupils of his mental age; on the other hand, if his 
achievement quotient is 75, we have evidence that he has achieved only 
seventy-five percent as much as the average of pupils of his mental age. 



35 





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37 



Table XI is to be used in obtaining the achievement quotients. Take, 
for example, a pupil who has a rate score of 165, a comprehension score of 
10, and an intelligence score of 60, An intelligence score of 60 is equivalent 
to a mental age of 11-6. (See Table VII). A rate score of 165 is equiva- 
lent to an achievement age of 12-6, and a comprehension score of 10 is 
equivalent to an achievement age of 11-0. To find the achievement 
quotient for rate of silent reading, find at the left of the table the line for an 
achievement age of 12-6 years. At the top of the table, find the column 
for a mental age of 11-6; follow down this column until you come to the 
line for 12-6. The number at this intersection point is the achievement 
quotient for rate. It is 109. To find the achievement quotient for com- 
prehension, follow down the same column until you come to the line for an 
achievement age of 11-0; the number at this intersection, 96, is the ac- 
chievement quotient for comprehension. 

Mental age norms versus chronological age norms. In determining 
a basis for translating point scores into age scores we have grouped the 
pupils according to their mental ages as given by the Illinois General In- 
telligence Scale. A grouping according to chronological age would have 
been more convenient. Theoretically, the same results should have been 
obtained because the average mental age of an unselected chronological age 
group is identical with the average chronological age of that group. The 
determining motive for devising a procedure for translating point scores 
into age scores was to secure a convenient method for obtaining an achieve- 
ment quotient. This quotient expresses the relation between a pupil's 
achievement and his individual achievement norm. A pupil's capacity 
to learn or his mental age is a much more potent factor in determining his 
achievement than is his chronological age. In interpreting achievement 
we must compare it with a pupil's capacity to learn. Hence, logically, 
a grouping of pupils according to mental age is to be preferred. However, 
since the same numerical results will be obtained from a chronological age 
grouping there is practical justification for using it because of the greater 
convenience. 

Justification of disregarding school grade in determining achievement 
ages. In determining the median point score of pupils having the same 
mental age no attention was given to the school grade to which the pupils 
belong. Pupils in the third grade were grouped with pupils in the eighth, 
providing they had the same mental age. This procedure implies that in 
judging a pupil's achievement his school grade may be disregarded. In 
other words, his achievement depends only or largely upon his mental 
age and upon the effectiveness of the instruction received, and not on the 
quantity of the instruction as measured by the grade attained. The valid- 
ity of this assumption was investigated by calculating separately for each 

38 



school grade the median achievement age scores for each mental age group. 
Figure 8 represents graphically these median achievement age scores for 
arithmetic in the Decatur schools. It will be noticed here that there is, 
in general, a distinct increase from grade to grade in the median point score 
of pupils belonging to the same mental age. Thus, in this case our assump- 
tion is not in entire agreement with the facts. However, convenience of 
use demands that we have only one rule for translating point scores into 
achievement ages. If a different one were used for each half grade or for 
each grade the inconvenience and confusion arising would decidedly limit 
the usefulness of the scale. Furthermore, any injustice which may be 
done to pupils in the lower grades may be compensated for in the interpre- 

Or 



18 

r7l- 

16 

IS ■ 

14 - 

13 

12 

11 

10 

9 

6 

7 



I 3d 




L-.L. 



& 



14 



16 



10 12 

MENTAL AGE 

FIGURE 8. EFFECT OF SCHOOL GRADE UPON ACHIEVEMENT IN 

ARITHMETIC. 

39 



tation of the achievement quotients. The grade norms, however, show 
that in general the increase from grade to grade is slight. (See page 66). 

Figures 9 and 10 report similar data for comprehension and rate of 
silent reading. In both of these figures it is practically impossible to dis- 
tinguish between the lines representing the median achievements in the 
lower grades and those representing the median achievements in the 
upper grades. Consequently, we may say that our assumption in the 
case of silent reading that we disregard the placement of the pupil in 
translating his point score into an achievement age score is closely in 
agreement with the facts. Another interpretation of these figures is that 
ability to read silently correlates highly with general intelligence. 




10 12 

MENTAL AGE 
FIGURE 9. EFFECT OF SCHOOL GRADE UPON ACHIEVEMENT IN COMPRE- 
HENSION OF SILENT READING. 



40 




10 12 

MENTAL AGE 



14 



16 



FIGURE 10. EFFECT OF SCHOOL GRADE UPON ACHIEVEMENT IN RATE 'OF 
SILENT READING. 



The Illinois Examination yields four age scores and four quotient 
scores for each pupil. Provision has been made to calculate an average 
score in the case of silent reading. When this is done each pupil has ten 
scores. Table XII gives representative scores. 



41 



c 
o 

& 



c 
■-3 



CA) 






o <u 



4-1 4-1 









OooO'— 'OoO'— ifSO'— it^^ 






c^ 



r^ cs -* O 



VO «N Q 

ooOOOnOOOcA'-'O 



oooocAoor^oor^r^'-iCAcs 



bO 



bo 

c 

■-5 



(r> 



0) 



a.2 

O V 



j=l.ii 



<e 



r^ONcor^vOTti^-HCir^oO'— I 



»-H »-H 1— ( 1—1 1—1 CS 






•-I •— 1 •-I CS 






CNCNOM^VOCS'-HOOt^'— iCSwn 



-a 

OS 






3 



'— icsco'<t'»o\or^oooNO'— icN 



42 



IV. FUNCTION. 

The function of the three scales which make up the Illinois Examina- 
tion is implied in their structure. The Illinois General Intelligence Scale 
provides a measure of general intelligence of children in grades III to VIII, 
inclusive.* Monroe's Standardized Silent Reading Tests, Revised, are 
intended to yield measures of the ability to read silently simple descriptive 
and narrative material when the reading is done for the purpose of an- 
swering questions. Monroe's General Survey Scale in Arithmetic is de- 
signed to yield general measures of a pupil's ability to perform the operations 
of arithmetic. It should be noted that the function of these tests is general 
rather than diagnostic. It is possible to use the sub-tests of the General 
Survey Scale in Arithmetic as diagnostic tests although they were not 
designed for this purpose. 

The function of the Illinois Examination as a whole is indicated in the 
introductory statement. 

V. VALIDITY 

The ideal procedure to be followed in studying the truthfulness of the 
measures yielded by the scales included in the Illinois Examination would 
be to compare them with true measures secured by other means. However, 
in no case are such true measures available. It is, therefore, necessary to 
study the validity of these scales by methods which are obviously imper- 
fect. 

1. Objectivity. The scales of the Illinois Examination are highly 
objective with respect to the scoring of test papers. Except when a 
pupil fails to follow directions no questions, concerning which answers are 
correct, arise. The administration of the tests is also highly objective. 
The directions for examiners have been found to be adequate and in all 
cases the examiner is told very explicitly what he is to say to the pupils. 
Much of the explanation is also printed on the test booklet so that the 
pupil has an opportunity to read as well as to hear the explanation. 

2. Reliability**. In order to study the reliability of the three scales 
which make up the Illinois Examination the different forms were given to 
the same pupils. The instruction to those cooperating in this study was 
to give all the forms within the same half day. The scores on the different 
forms were compared by means of the Pearsonian coefficient of correlation 
and by means of other statistical devices which will be explained in the 
following pages. 



*It is also recommended for use in the high school. 

**A related phase of reliability is considered on page 68 under the head of "Practice 
effect when test is repeated." 

43 



The coefficient of correlation merely indicates the relationship between 
two sets of scores. It is simply an index of the extent to which the pupils 
make the same score on the second trial of a test that they make upon 
the first trial when the practise effect is disregarded. In Figure 11, we 
represent graphically the scores made by the fifth grade pupils on Forms 
1 and 2 of the Illinois General Intelligence Scale. The coefficient of 
correlation for this group of scores is .92 ± .006. It is obvious that in 
some cases the pupils make the same score or approximately the same score 
on second trial. In other cases there are marked differences between the 
scores on the two trials. 

In Figure 11 the regression line, y = 4.92 + -80 x, has been drawn. 
Perfect correlation (ri2 =1.00) would be secured if the Form 1 scores 
were changed so that all points would fall upon this regression line. This 
would require a vertical shifting of the points. Those above would be 
moved downward, while those below would be moved upward. For a few 
of the points vertical lines have been drawn in to indicate the amount of 
shifting necessary. Perfect correlation would be secured if this were done 
with reference to any line but this regression line is the one for which the 
standard deviation of the shifting is the least. The other regression 
equation, x = 4.69+1.05 y, possesses similar properties for a horizontal 
shifting. 

The amounts of changes necessary to secure perfect correlation may 
be thought of as departures from perfect correlation. The magnitude of 
these changes is described by the equation for the probable error of 

estimate, 

P.E.est = .6745(ry\/l — r'i2. 
Substituting in this equation for cry and ri2 we have the probable error 
of estimate equal to 6.06. The probable error of estimate is more easily 
interpreted as the index of the degree of correlation that exists than as 
the coefficient of correlation. 

Since neither set of scores gives accurate measures of intelligence the 
differences between the pairs of scores do not truthfully represent the de- 
gree of inaccuracy of either set of scores. The error of any score is the 
difference between it and a pupil's true score. We may define a true score 
as the average of an infinite number of scores after they have been corrected 
for practise effect, fatigue, and other factors which would tend to increase 
or decrease the averages of the successive sets of scores. Such true scores 
are obviously not obtainable. It is, however, possible to determine the 
coefficient of correlation between either set of obtained scores and the 



44 



corresponding true scores. This is done by the formula,* 



FORM I 

\zo- 



114 
106 
\0Z\ 

96 

90 

64. 

76 

72 

66 

eo 

54 
46 
AZ 
36 
30 
24 
IS • 



12 - 



r».92 ±006 
C;= 26.40 0-^=23.05 
AVx=6J.6 AV.^=54.2 
Dx = 1.05 by = .60 
X =469 +I.05Y 
Y = 4.92+. 80 X 



{io4,iia) 



30 



6 • 

(86,66) 



•iiofizY 



7 
/'75,5a) 



/ X (54,50) 



\<o 



(5 



i^l.zo) 



12 



2A- 



36 



46 



72 



64 



96 



\0& 



\Z0 



60 
FORM 2 
FIGURE 11. CORRELATION OF FORM 1 SCORES WITH FORM 2 SCORES OF THE 
ILLINOIS GENERAL INTELLIGENCE SCALE, FIFTH GRADE. 

In this formula ri2 is the coefficient of correlation between the two sets of 
obtained scores and rit is the coefficient of correlation between one set of 
obtained scores and the corresponding true scores. To distinguish^ the 

*See Kelley, T. L. "A simplified method of using scaled data for purposes of testing," 
School and Society, 4:74, July 8, 1916, and "The reliability of test-scores," Journal 0/ Educa- 
tional Research, 3:370-79, May, 1921. 

45 



coefficient of correlation of a set of obtained scores with the corresponding 
set of true scores from the coefficient of correlation between two sets of 
obtained scores we call the latter the coefficient of reliability and the 
former the index of reliability. 

Table XIII gives coefficients of reliability (ri2) for each of the three 
scales which make up the Illinois Examination. Table XIV gives the 
corresponding indices of reliability (ru). It will be noted that a high 
degree of reliability is indicated in most cases. In some instances it is un- 
usually high in comparison with the degree of reliability reported for other 
tests. In the case of silent reading certain instructions were not followed 
by some of the examiners, and it is thought that their failure to do so caused 
the two sets of scores to correlate less highly than they should. 

Both the coefficient of reliability and the index of reliability are diffi- 
cult to interpret. They express a general relationship but not in terms of 
the actual amount of error which must be allowed for in the case of the 
scores of individual pupils. It is possible to calculate another and more 
easily interpreted expression of the reliability or accuracy of the measures 
yielded by tests. The probable error of estimate is given by the formula, 



P.E.est = .6745o-\/l — rV 

In the formula d may be taken as either cti or cr^. Theoretically, 
these are expected to be equivalent. Practically, slight differences may 
exist. It is, therefore, advisable to use as the value of a the average of 
(Tx and 0-2. The probable error of estimate (P. E. est) in this case is 
essentially the probable error in the measurements yielded by the test. 
Hence, we call it by this name and use the symbol, P. E.^. Since 
rit=\/ri2, the above formula may be written in the form, 
P.E.n. = .6745(T\/l — ri2. 

The probable error of measurement calculated by the above formula is 
to be interpreted as an index of the amount of departure of the obtained 
scores from the true scores. In other words, it is the error which the ob- 
tained score involves. This error is described as a probable error. Such 
a description, of course, tells us nothing about the magnitude of the error 
in the case of a particular pupil but it does describe in a general way the 
magnitude of the errors involved in a group of scores. 



•46 



TABLE XIII. RELIABILITY COEFFICIENTS 







General 


Arithmetic 


Silent Read 


ng 






Intelligence 












Grade 


Form 




























Com- 






No. of 


ri2 


No. of 


ri2 


No. of 


Rate 


prehen- 






Pupils 




Pupils 




Pupils 


ri2 


sion ri2 


III 


1 with 2 

2 with 3 
1 with 3 


76 


.86 


299 


.80 


116 


.69 

.72 
.72 


.63 
.64 
.63 


IV 


1 with 2 

2 with 3 
1 with 3 


120 


.93 


271 


.86 


112 


.79 
.80 
.70 


.63 

.64 
.60 


V 


1 with 2 

2 with 3 
1 with 3 


243 


.92 


256 


.88 


120 


.79 
.86 

.72 


.69 
.74 

.71 


III 


1 with 2 






826 


.95 


348 


.78 


.80 


to 


2 with 3 












.85 


.64 


V 


1 with 3 












.76 


.82 


VI 


1 with 2 

2 with 3 
1 with 3 


198 


.82 


271 


.76 


139 


.87 
.89 
.90 


.52 
.86 
.70 


VII 


1 with 2 

2 with 3 
1 with 3 


157 


.80 


257 


.71 


100 


.72 
.74 
.61 


.68 
.75 
.63 


VIII 


1 with 2 

2 with 3 
1 with 3 


164 


.67 


171 


.79 


119 


.91 
.88 
.91 


.85 
.71 
.85 


VI 


1 with 2 






699 


.76 


358 


.79 


.72 


to 


2 with 3 












.84 


.76. 


VIII 


1 with 3 












.75 


.76 


III 


1 with 2 


958 


.92 












to 


















VIII 



















47 



TABLE XIV. INDEX OF JIELIABILITY 







General 


Arithmetic 


Silent Reading 






Intelli 


gence 












Grade 


Form 




























Com- 






No. of 


rit 


No. of 


rit 


No. of 


Rate 


prehen- 






Pupils 




Pupils 




Pupils 


rit 


sion rit 


III 


1 with 2 

2 with 3 
1 with 3 


76 


.93 


299 


.89 


116 


.83 
.85 
.85 


.79 
.80 
.79 


IV 


1 with 2 

2 with 3 
1 with 3 


120 


.96 


271 


M 


112 


.89 
.89 
.84 


.79 
.80 

.77 


V 


1 with 2 

2 with 3 
1 with 3 


243 


.96 


256 


.94 


120 


.89 
.93 
.85 


.83 
.86 
.84 


III 


1 with 2 






826 


.97 


348 


.88 


.89 


to 


2 with 3 












.92 


.80 


V 


1 with 3 












.87 


.91 


VI 


1 with 2 

2 with 3 
1 with 3 


198 


.91 


271 


.87 


139 


.93 
.94 
.95 


.72 
.93 
.84 


VII 


1 with 2 

2 with 3 
1 with 3 


157 


.89 


257 


.84 


100 


.85 
.86 
.78 


.82 
.87 
.79 


VIII 


1 with 2 

2 with 3 
1 with 3 


164 


.82 


171 


.89 


119 


.9S 
.93 
.95 


.92 
.84 
.92 


VI 


1 with 2 






699 


.87 


358 


.89 


.85 


to 


2 with 3 












.92 


.87 


VIII 


1 with 3 












.87 


.87 


III 


1 with 2 


958 


.96 












to 


















VIII 



















4^ 



TABLE XV. PROBABLE ERRORS OF MEASUREMENT AND RATIO OF PROBABLE 
ERRORS OF MEASUREMENT TO AVERAGE SCORES 




Forms 


Intelligence 


Arithmetic 




Silent I 


leading 
Ra 




Grade 


IT •±_j»m 


P.E.„ 


P.E.^ 


P.E.n. 


Compre 


hension 


Lte 


P.E.„, 


P.E.„, 


P.E.n. 


P.E.^ 




Av. 


Av. 




Av. 


Av. 


III 


I with 2 

1 with 3 

2 with 3 


3.5 


0.10 


2.6 


0.17 


1.2 
1.3 
1.3 


0.16 
0.17 
0.17 


13.7 
13.7 
14.5 


0.12 
0.11 
0.12 


IV 


1 with 2 

1 with 3 

2 with 3 


S.5 


0.09 


4.6 


0.12 


1.4 
1.2 
1.2 


0.16 
0.14 
0.13 


10.3 
12.8 
10.9 


0.08 
0.10 
0.09 


V 


1 with 2 

1 with 3 

2 with 3 


4.7 


0.08 


4.4 


0.09 


1.2 
0.9 
1.1 


0.10 
0.07 
0.09 


12.0 
13.7 
10.7 


0.08 
0.08 
0.07 


III 

to 

V 


1 with 2 

1 with 3 

2 with 3 






3.2 


0.10 


1.0 
1.0 
0.9 


0.11 
0.10 
0.09 


13.1 
13.7 
11.5 


0.10 
0.10 
0.08 


VI 


1 with 2 

1 with 3 

2 with 3 


5.5 


0.07 


6.3 


0.10 


1.3 
1.1 
1.1 


0.10 
0.09 
1.08 


9.1 
8.2 
9.5 


0.05 
0.05 
0.05 


VII 


1 with 2 

1 with 3 

2 with 3 


6.4 


0.07 


5.3 


0.09 


1.2 
1.4 
1.1 


0.09 
0.10 
0.07 


13.6 
17.0 
14.9 


0.07 
0.09 
0.07 


VIII 


1 with 2 

1 with 3 

2 with 3 


7.7 


0.08 


5.4 


0.08 


0.8 
0.9 
1.1 


0.05 
0.06 
0.07 


7.5 
7.5 
9.8 


0.04 
0.04 
0.05 


VI 

to 
VIII 


1 with 2 

1 with 3 

2 with 3 






6.2 


0.10 


1.1 
1.1 
1.1 


0.08 
0.08 
0.08 


12.0 
13.7 
11.4 


0.07 
0.07 
0.06 


III 

to 
VIII 


1 with 2 


5.3 


0.07 















49 



The probable error of measurement tends to increase as the scores 
become larger and the significance of an error depends upon the magnitude 
of the score with which it is associated. For this reason added meaning 
can be given to our description of the errors by calculating the ratio of the 
probable error of measurement to the average score. This gives the 
probable error of measurement in the form of a percent of the score. In 
Table XV, the probable errors of measurement and the ratios of these to 
the average scores are given. The numbers of pupils involved are the 
same as those given in Tables XIII and XIV. A probable error of measure- 
ment of 3.5 for the Illinois General Intelligence Scale in the third grade 
means that the point scores of fifty percent of the pupils will involve errors 
less than this amount. The remaining fifty percent of the scores will in- 
volve errors greater than 3.5. A somewhat more general statement is 
that, on the average, the scores obtained from third grade pupils will in- 
volve probable errors of ten percent of their magnitude. The larger the 
score the larger the probable error. 

The magnitude of these probable errors of measurement may appear 
to be somewhat disturbing but they are not large in comparison with those 
calculated for other tests. In the case of the Illinois General Intelligence 
Scale the average probable error of measurement amounts to about six 
months. This is approximately the same as that calculated for the 
Stanford Revision of the Binet Scale for the Measurement of Intelligence.* 
An unpublished study of the reliability of a group of silent reading tests 
made by the writer gave ratios of reliability which are much larger in many 
cases. 

3. Discrimination. The shape of the distribution of the scores which 
a test yields throws some light upon its validity. In order that a test be 
valid the scores must show differences of the traits measured when these 
differences exist. When a representative group of pupils is measured with 
reference to a mental or a physical trait we may expect to find a distribu- 
tion closely approximating the normal shape. When the number of cases 
is large this approximation should be close if there is proper discrimina- 
tion. Any marked departure from the normal shape indicates that for 
some pupils at least there is a lack of discrimination. On the other hand, 
when we have a normal distribution we cannot know definitely that our 
measures are accurate. The shape of the distribution, therefore, has only 
a negative significance. We can only say that when there is a striking 
departure from normality there is a lack of discrimination and, hence, in- 
accuracy of measurement for some pupils. 



*Otis, A. S. and KnoUin, H. E. " Reliability of Binet Scale and Pedagogical Scales." 
Journal of Educational Research, 4:121-43, September, 1921. 

50 



Figures 12, 13, 14, and 15 represent graphically the distributions of 
scores yielded by the scales of the Illinois Examination for certain groups 
of pupils. In Figure 12, the distributions with respect to mental age are 
given for grades IV, VI, and VIII. Each of these distributions includes 
several thousand children. They have been reduced to the same basis 
by expressing the frequencies in terms of percents. Each of these curves 
closely approximates the normal distribution. Thus, in the case of the 
Illinois General Intelligence Scale, the shape of the distributions furnishes 
no evidence that there is a lack of discrimination. 

In Figures 13, 14, and 15, we give the distributions of the achievement 
ages for grades III, V, VI, and VIII, for the pupils of one city. Because 
the original bases for translating point scores into achievement ages were 
found to be incorrect it is not possible to use the scores of the pupils on 
which the distributions for mental age given in Figure 12 are based. The 
distributions of achievement ages in arithmetic (Figure 13) exhibit striking 
departures from the normal shape in grades III and V. In grades VI and 

PERCENT 



•4 



12 - 



10 



rn 



GRADE TZ" 
M "EDI 




6 



10 



12 14. 16 

MENTAL AGE 

FIGURE 12. DISTRIBUTION OF PUPILS ACCORDING TO MENTAL AGE. 

SI 



PUPILS 
ISOf 



100 

so 



zoo 

ISO 
100 
50 






ZOOr. 

150- 
100 - 

50' 
- 
400 r 
350- 
300- 
250- 
ZOO- 

150 ■ 

too- 

50- 
O- 



FIGURE 
AGE 



a 



j-^ 



GRADE "Sni 



iO 12 14 16 16 20 







1 


GRADE 


•St 






































1 




1 r 


- 




, 




1— 


— 1 1 b_. 



6 10 12 



■^ 



8 10 



4 16 18 20 



GRADE Y 



12 14 16 



16 20 



GRADE m 



=< I I L. 



6 \0 12 14 (6 IS ZO 

ARITHMETIC AGE 
13. DISTRIBUTION OF PUPILS ACCORDING TO ACHIEVEMENT 
IN ARITHMETIC. 

52 



PUPILS 
120 



GRADE TZni 




6 6 \0 12 14 16 16 20 22 



GRADE YL 




14 16 16 20 22 



I60r 

izoh 

80 
40 



240 
200 

\eo 

120 

60 
40 



1 I t I I t 



GRADE Y 



■ ' ' I I L 



10 



\Z 



14 



(6 



(6 



20 



22 



GRADE m 



I I I I L 



a 



10 



1 i I 1 L. 

zo 



22 



\Z \A 16 la 

COMPREHENSION AGE 
FIGURE 14. DISTRIBUTION OF PUPILS ACCORDING TO ACHIEVEMENT AGE 
IN COMPREHENSION OF SILENT READING. 

S3 



PUPILS 
lOO 




\50 
\Z5 
\0O 

175 

50 

25 


200- 

175- 

ISO 

\25 

\00 

75 

50 

Z5 

O 



6 8 \0 \Z 



14 16 16 ZO ZZ 



GRADE Y 




' ' I 1 1 — 



10 



\z 



14 



16 



18 



20 



ZZ 



6RA0E HI 



6 



JO 



16 



16 



20 



22 



\Z 14 

FIGURE 15 DISTRIBUTION OF PUPILS ACCORDING TO ACHIEVEMENT AGE 
IN RATE OF SILENT READING. 

54 



VIII the resemblance to the normal curve is very close. It will be re- 
membered that in measuring achievement in the field of arithmetic one 
scale is used for grades III, IV, and V,and another for grades VI, VII, and 
VIII. It appears, therefore, that the scale designed for use in the lower 
grades does not measure accurately the arithmetical abilities of some 
pupils in the lower grades. The fact that such a large percent of pupils 
in these grades are grouped together shows that this scale fails to discrimi- 
nate between some pupils having different degrees of ability. 

Figure 14 gives the corresponding distributions for comprehension of 
silent reading. These distributions more nearly approach the normal 
shape. The one for the sixth grade exhibits two modes. In each grade 
there are a few very high scores which destroy the symmetry of the figures. 

In Figure 15, we represent graphically the corresponding distributions 
for rate of silent reading. These graphs exhibit striking departures from 
the normal shape, particularly in the upper grades. It is clear, therefore, 
that in the case of rate of silent reading the measures must be considered 
lacking in accuracy in a number of cases. In the eighth grade, particularly, 
there is a failure to discriminate with respect to the rate of reading in the 
cases of many pupils who read rapidly. This tendency is also seen in the 
other grades. The irregularities are probably due in part to the fact that 
rate of reading the unconnected exercises varies from exercise to exer- 
cise. Some may be read rapidly, others very slowly. 

In Figure 4 we gave the total distribution of the intelligence quotients 
for the pupils in grades IIIB to VIIIA, inclusive, in a large city school 
system. (See page 29). This distribution approximates the normal dis- 
tribution very closely except for the interval from 90 to 100. The fre- 
quency in this interval is less than that for the intervals on either side. 
This, however, is probably due to the use of our table to calculate the 
I. Q.'s. 

For the achievement quotients we give only the distributions for all 
grades combined. The distributions for the separate grade groups do not 
show any marked irregularities. In Figure 16, the distribution of the 
achievement quotients for arithmetic is given. This closely approximates 
the normal shape. This close approximation will also be observed in 
Figure 17 in the case of comprehension of silent reading. For the rate of 
silent reading (See Figure 18) the distribution is less symmetrical, as we 
might expect after noting the irregularities in Figure 15. 



55 



An examination of the distributions of the intelligence quotients and 
of the achievement quotients does not reveal any indication of a marked 
lack of discrimination except possibly in the case of the rate of silent reading. 
One might be inclined to conclude that there was evidence of a lack of 
discrimination in the case of the intelligence quotient if the distributions 
for mental age did not approach the normal curve as closely as they do. 



PUPILS 

l2Q0r 



1000 
600 

600 
400 

200 




4-0 



60 



60 



160 



180 ZOO 



100 120 140 

ARITHMETIC AQ. 
FIGURE 16. DISTRIBUTION OF PUPILS ACCORDING TO ACHIEVEMENT 
QUOTIENTS IN ARITHMETIC. 



PUPILS 
1200 r 



1000 
600 
600 
400 
ZOO 



40 SO 60 100 120 \A0 

COMPREHENSION A.Q. 



\60 



\eo 



ZOO 



FIGURE 17. DISTRIBUTION OF PUPILS ACCORDING TO ACHIEVEMENT 
QUOTIENTS IN COMPREHENSION OF SILENT READING. 



PUPILS 

600 r 



600- 



400 




200- 



60 60 \0O \20 J40 \60 160 ZOO ZZO 240 260 Z&Q 

RATE AQ. 
FIGURE 18. DISTRIBUTION OF PUPILS ACCORDING TO ACHIEVEMENT 
QUOTIENTS IN RATE OF SILENT READING. 

4. Comparison with criterion measures. The Illinois General In- 
telligence Scale was given to 203 pupils whose mental ages had also been 
determined by the Stanford Revision of the Binet Scale for Measuring In- 
telligence. The correlation between the mental ages determined by these 
two scales is .74 ± .02. The probable error of estimate is 1.2 years. 
This means that in 50 percent of the cases, the mental age, as determined 
by the Illinois General Intelligence Scale, differed from that as determined 
by the Binet Scale by 1.2 years or less. This lack of agreement between 
the measures secured by these two scales is not due solely to errors in the 
measures yielded by the Illinois General Intelligence Scale. The Stan- 
ford Revision of the Binet Scale for Measuring Intelligence also yields 
measures which involve errors of approximately the same magnitude as 
those of the Illinois General Intelligence Scale. (See pages 24-27). 

In November, 1920, both the Illinois General Intelligence Scale, 
Form 1, and the National Intelligence Scale, Form 1, were given to 3615 
pupils in eight elementary schools in Chicago. The correlation between 
the scores obtained from these two tests is indicated in Table XVI. The 
probable errors of estimate indicate that the agreement is not close. The 
probable error of estimate, when all grades are taken together, is 11.5. 



57 



This means that the departure from perfect correlation with the scores 
yielded by the National Intelligence Scale is greater than 11.5 points in 50 
percent of the cases, and less than 11.5 in 50 percent of the cases. Since 
ten points are equivalent to one year of mental age, the relationship be- 
tween the scores yielded by the Illinois General Intelligence Scale and by 
the National Intelligence Scale is approximately the same as the relation- 
ship shown to exist between the scores yielded by the Illinois General In- 
telligence Scale and the Stanford Revision of the Binet Scale for Measur- 
ing Intelligence. 

TABLE XVI. CORRELATION BETWEEN SCORES YIELDED BY ILLINOIS GENERAL 
INTELLIGENCE SCALE AND BY NATIONAL INTELLIGENCE SCALE 





Number of 






P.E.est 


Grade 


Cases 




P.E.e,t 






Aver. 


III A 


357 


0.53 


9.1 


0.22 


IV B 


416 


0.70 


9.6 


0.18 


IV A 


335 


0.74 


8.0 


0.14 


VB 


460 


0.55 


8.7 


0.14 


VA 


285 


0.47 


12.0 


0.19 


VI B 


383 


0.44 


12.6 


0.17 


VIA 


259 


0.67 


10.8 


0.13 


VII B 


350 


0.70 


11.0 


0.12 


VII A 


210 


0.68 


10.3 


0.11 


VIII B 


271 


0.72 


10.2 


0.10 


VIII A 


289 


0.69 


10.9 


0.10 


All Grades 


3615 


0.81 


11.5 


0.16 



The Illinois General Intelligence Scale, Form 1, was given to a number 
of sixth-grade pupils whose I. Q.'s, as determined for the Otis Group In- 
telligence Tests, were available.* The coefficient of correlation for 83 
VIA pupils was .82±.02. For 124 VIB pupils the value of r was .83±.02. 
The probable error of estimate was 6.4 in the first case and 5.9 in the latter. 

The Pintner Non-Language Group Intelligence Tests are represented 
to have a reliability coefficient of .72. This is by mental indices and 
not by point scores. The two sets of measures were obtained by use of the 
same test after an interval of two years. The number of children tested 
was 46. These group intelligence tests were also given during the same 
semester to 300 children whose mental ages had been determined by the 
Stanford Revision of the Binet Scale for Measuring Intelligence. The 



*The writer is indebted to Superintendent L. W. Keeler, Michigan City, Indiana for 
these data. 

S8 



coefficient of correlation between the point scores yielded by the Pintner 
Group Test and the mental ages determined by the Binet Test was .80.* 

No data are available at this time for making comparison between 
the measures of achievement yielded by the achievement scales included 
in the Illinois Examination and by other similar scales. Neither are data 
available for comparison of measures of achievement with teachers' esti- 
mates. 

5. Inferences concerning validity based upon the structure of the 
test and its administration. In the case of the Illinois General Intelligence 
Scale the sub-tests have frequently been used by other makers of instru- 
ments for measuring general intelligence. At the time the Illinois General 
Intelligence Scale was constructed a number of other intelligence scales 
were analyzed with reference to sub-tests and the ones most frequently 
found were incorporated in this scale. 

The intercorrelations between the seven sub-tests were studied by 
choosing at random two sets of 120 test papers each. In securing these 
samples ten papers were chosen from each half grade. The correlation of 
each sub-test with each other sub-test and with the total test score is given 
in Table XVII. The upper number in each case refers to the first sample 
and the lower to the second sample. It will be noted that the correlation 
of a sub-test with the total score is higher than the correlation with the 
other sub-tests. The correlations with the total score are high in every 
case. Sub-tests 2 and 3 have the highest coefficients of correlation. The 
intercorrelations between the sub-tests are relatively high but it must be 
remembered that we have used a wide range of talent extending from IIIB 
to VI 1 1 A. The table, however, is evidence that the overlapping between 
the sub-tests is not great and is approximately uniform. 

It is interesting to note the differences between the corresponding 
coefficients yielded by the two samples. The differences are never large 
and are within the range indicated by the probable errors of the coefficients 
of correlation due to sampling. 

The Illinois General Intelligence Scale is explicitly a verbal test. 

Ability to read is a prerequisite. For this reason it may be urged that it 

does not permit non-verbal elements of intelligence to function. This 

objection, of course, applies to other verbal tests. No data are at hand to 

show the limitation which this feature places upon the scale. 

The silent reading test included is a revision of Monroe's Standardized 

Silent Reading Test. In this revised form certain features of the original 

test which were found unsatisfactory have been eliminated. The scoring 

has been made objective. The exercises are more uniform and a more 

*Pintner, Rudolph and Marshall, Helen. "Combined mental-educational survey." 
Journal of Educational Psychology. 12:32-43, January, 1921 . 

59 



TABLE XVII. INTERCORRELATIONS BETWEEN THE SUB-TESTS OF THE ILLI- 





NOIS GENERAL INTELLIGENCE SCALE, FORM 


I=K 




Sub- 
Tests 


Sub-Tests 


1 


2 


3 


4 


5 


6 


7 


Total 


1 




.58 
.68 


.63 

.73 


.51 
.48 


.51 
.44 


.57 
.60 


.56 
.62 


.77 
.84 


2 


.58 
.68 




.74 
.75 


.65 
.60 


.49 
.61 


.67 
.73 


.64 
.70 


.83 
.89 


3 


.63 

.73 


.74 

.75 




.63 
.61 


.57 
.70 


.64 

.72 


.68 
.76 


.88 
.93 


4 


.51 
.48 


.65 
.60 


.63 
.61 




.41 
.50 


.58 
.55 


.52 

.54 


.77 
.78 


5 


.51 
.44 


.49 
.61 


.57 
.70 


.41 
.50 




.51 
.51 


.47 
.57 


.70 

.77 


6 


.57 
.60 


.67 
.73 


.64 

.72 


.58 
.55 


.51 
.51 




.55 
.61 


.79 
.80 


7 


.S6 
.62 


.64 
.70 


.68 
.76 


.52 
.54 


.47 
.57 


.55 
.61 




.79 
.86 


Total 
Score 


.77 
.84 


.83 
.89 


.88 
.93 


.77 
.78 


.70 

.77 


.79 
.80 


.79 
.86 





*Two coefficients are given for each pair. Each was calculated from a random selec- 
tion of ten test papers from each half grade group III B to VIII A, inclusive. 

precise measurement of the rate of silent reading is secured. Experience 
has shown that the test is too short for the time limit allowed. This, in 
the case of the most fluent readers, prevents one from securing valid meas- 
ures of reading ability. To one acquainted with the nature of reading 
ability and its measurement, this one test obviously measures in a general 
way, only one type of silent reading ability. To measure completely 
all phases of silent reading ability would require a battery of tests. 

In the case of Monroe's General Survey Scale in Arithmetic the sub- 
tests are judged to represent the most important types of examples learned 
by pupils in the sequence of grades for which they are intended. The 
choice represents the judgment of the author but is not inconsistent with 
other groups of tests used to measure ability of pupils in the operations ot 
arithmetic. A single general score has been used to describe the pupil's 

6o 



ability. This is, obviously, a composite not only of the scores of the different 
sub-tests but also of the dimensions of rate and accuracy. However, 
since a single general measure is desired this does not constitute a serious 
criticism of the scale. 

Summary for validity. By way of summary we may say that the 
scales which make up the Illinois Examination compare fa^^'orably in 
respect to validity with our best tests. It is, however, clear that the 
scales possess certain limitations which should be kept in mind when the 
scores are interpreted. 

VI. VALIDITY OF SIGNIFICANCE 

Probably all readers will admit that the abilities measured by this 
battery of tests are important in the education of children. They are 
probably the abilities most often measured. The Illinois Examination 
includes a plan, however, for combining measures of intelligence and 
measures of achievement. It is, therefore, appropriate that we point out 
the significance of the comparison proposed. 

Significance of achievement quotients. In Figure 19, the achieve- 
ment ages for both arithmetic and reading average are shown for City A 
and City B. It is clearly evident, from this figure, that when considered 



ARITHMETIC 



READING AVERAGE AGE 




GRADE. 



Y "21 
GRADE 



FIGURE 19. ACHIEVEMENT AGES FOR ARITHMETIC AND FOR READING 
(AVERAGE) FOR CITY A AND CITY B. 

6l 



grade for grade, City B is distinctly superior to City A in both arithmetic 
and reading. The superiority is more pronounced in the case of reading. 
If this were the only information at hand for these two cities the con- 
clusion would be that the schools of City B were superior to those of 
City A, and that City A was below the city average. 

In Figure 20, the median mental age and the median I. Q. for the sever- 
al grades of these two cities are represented. The school system in City 
B is shown to have been so organized that in each grade the median mental 
age of the pupils is about one year greater than in City A. The median 
intelligence quotients are also distinctly higher. In fact, City B, except in 
the third grade, is distinctly above the city average. These facts mean 
that, grade for grade, City B has superior pupil material. This is probably 
due to a difference in the organization of the school systems of the two 
cities. In City B, the school system is so organized that in the upper 
grades the pupils are highly selected. In City A, the opposite condition 
prevails. Therefore, we should expect City B to secure distinctly superior 
achievements, grade for grade. 



MENTAL AGE 






/ / 
' / / 


/ 
/ 

/ / 


// 
/ 


/// 




/// 


// 1 




• CITY Avei?. 
- CITY A. 
■ CITY B. 


/ 


1 
t . 


IK ET Y Y[ 
GRADE 


"sn "SHE 



INTELLIGENCE QUOTIENT 



MA. 
15 



14 

13 

12 

II 

10 
9 
6 
7 



FIGURE 20. MEDIAN MENTAL AGE AND MEDIAN I. Q. FOR EACH GRADE 
FOR CITY A AND CITY B. 




62 



We now have to answer the question, "Is the school system of City 
B as effective as that of City A when the character of the pupil material in 
the two cities is taken into account." Figure 21 answers this question. 
It shows the achievement quotients for these two cities. In the case of 
arithmetic the quotients for City B are, except in the eighth grade, below 
those for City A. They are also below the city average. In the case ot 
reading City B surpasses City A only in the seventh and eighth grades. 
Therefore, we must conclude that, with the exception of the eighth grade 
and in part the seventh, the school system of City B is less effective in the 
teaching of the operations of arithmetic and silent reading than the school 
system of City A. By using the mental ages of the pupils we have thus 
been able to avoid an erroneous interpretation of the measures of achieve- 
ment for these two cities. 



ARITHMETIC QUOTIENT 




n 



ET 



CfTY AVER. 
CITY A. 
CITY B. 



T H 
GRADE 



"nr ini 



Afl. 
106 



104 
102 
\00 
96 
96 



94. 



92 



READING AVERAGE <aUOTIENT 




CITY AVER. 



CITY A. 

— CITY B. 



L-L 



n 



w 



Y H 
GRADE 



m UK 



FIGURE 21. ACHIEVEMENT QUOTIENTS FOR EACH GRADE FOR CITY A 
AND CITY B. 

A pupil's mental age constitutes an individual norm with which his 
achievement ages may be compared. The results of this comparison are 
expressed by the achievement quotients. The value of individual norms 
and the achievement quotient are illustrated by Figure 22. This figure 

63 



shows the point scores and the achievement quotients for comprehension 
of silent reading of the pupils in a fifth-grade class. The former are 
plotted along the horizontal axis and the latter along the vertical axis. 
Distances of a dot from the two axes show the two measures of the pupil's 
achievement. The grade norm in terms of a point score is indicated by 
the arrow. 

200- 
190- 
180- 
170- 
\60- 
ISO - 
140- 
130 - 

120- . ;. . . 

wo ■ . 



\00 

90 

60 

10 

60 - Sfandard 

50 

FIGURE 22. RELATION BETWEEN POINT SCORES AND ACHIEVEMENT 
QUOTIENTS IN COMPREHENSION OF SILENT READING, A FIFTH GRADE 
CLASS. 

The lowest score in the class is four. If we had only the grade norm, 
all we could say about this pupil would be that he is conspicuously below 
standard and at the foot of his class. His A. Q. shows that in comparison 
with his own norm he has achieved more than is usually achieved by a pupil 
of his mentality. In fact when his mental age is considered, he is one of 
the "good" pupils in his class. 

An added advantage of this plan is that when we have transmuted 
point scores in subject-matter tests into achievement ages, we have re- 
duced them all to the same units in the sense that each successive year 
corresponds to an increment of ability gained by typical children in equal 

64 



10 II 1^ 13 14 15 16 



lengths of time. Since the achievement ages are expressed in the same 
imits, they may be combined as point scores cannot be combined. For 
example, we have no obvious way of expressing the total achievement of a 
child who scores 155 in rate, 11 in comprehension, and 49 in arithmetic. 
By reference to Table XI, however, we observe that these point scores 
indicate, respectively, achievement ages of 12-6, 11-6, and 10-6 years. On 
the assumption that the abilities to which the point scores refer are all 
equally important, we may obtain the simple average of these ages, and 
we may thus express the composite achievement age as 11-6 years. 

The translation of the point scores into age scores makes the measures 
more easily interpreted. Even without access to grade norms one is able 
to interpret partially a mental age of 13 or an achievement age of 9 years, 
6 months. The quotients are also easily interpreted because in every case 
the norm is approximately 100. 

The grade norms in the case of the achievement test do furnish appro- 
priate educational objectives. The norms for the intelligence scale can- 
not, of course, be considered objectives because of the assumption that 
traits measured by this scale are not covered by school instruction. 

VII. NORMS 

For the Illinois Examination two types of norms are available: age 
norms and grade norms. The Illinois General Intelligence Scale has been 
Standardized with respect to chronological age and the achievement 
tests with respect to mental age. Both the age scores and quotients have 
been standardized with respect to school grade. Thegrade norms are given 
in Table XVIII. The age norms are incorporated in the rules for trans- 
lating the point scores into age scores. In both cases the norms are for 
first /rial scores only. When the tests are repeated these norms should not 
be used. (See page 68). The grade norms for both ages and quotients 
are given in Table XVIII for three population groups; rural schools, city 
schools, and a general group, including city, town, and rural schools. The 
median scores for any grade or any city may be compared with these grade 
norms. It is helpful to make this comparison by expressing the median 
scores as deviations from these norms. When the median score is larger 
than the corresponding grade norm the deviation is positive, when less, 
negative. In Table XIX the median scores for a city are expressed as 
deviations from the grade norms. In the case of ages, the deviations are 
in terms of months: -6 indicates that the median age for this city is a halt 
year below the grade norm, +8 that it is eight months above the grade 
norm. 



65 



c« 

4-1 

c 

.a 

o 

& 


too 

c 

■-3 
<u 

4-1 

c 




4-1 

Pi 


^ CO ^ 

ooo 


t-- CN ^ 

0>00 


r>. n (^ 

ONOON 

1-H 


0\ 1-4 o 

OnOO 

1-H 1-H 


OOO 


OOO 


1 

S 
o 
U 


C 

o 

c 
v 

S2. 


^ CO 1—1 

OOO 

.— < i-H T— 1 


vO COO 

OnOO 

T— 1 1—1 


VO oo r-H 
ONOO 

y—k 1— 1 


^ ""f l-H 

ONOO 

1-H 1-H 


OOO 


t^QOO 

0\0 ON 


tiO 

c« 

ID 
> 
< 


.-H CO ^ 

OOO 

1-H T— ( »— 1 


r-- CO 1-1 

OnOO 

1—4 1— ( 


vT) «^ O 
OnOO 

1— C 1— ( 


NOCO^ 

c^o o 

1—1 1-H 


O 1-^ 1— ' 

OOO 


OOO 

1— 1 1-H t-H 


< B 


(N C>\ CN 

OOnO 

r— ( T— 1 


o\r-- oo 

ON C^ C\ 


■^ <N C^ 

OOO 


(N fS »-i 

OOO 

1-H 1-H 1-H 


OOO 


CO O --< 
OOO 

1—1 1-H 1-H 


Intelli- 
gence 


00\0 

CA OO o^ 


VO W-» lo 

On CTn On 


oo On oo 
ON On 0\ 


OOO 


OOO 


222 


to 

< 


60 

c 
'-5 

4.) 

c 


4-1 

ff5 


T— 1 1-H 

^ CS »-i 

1 1 1 

t^ oor^ 


1— 1 r^ lo 

1 1 1 

On C7\ On 


10-2 

10-10 

10-7 


^77 

1— 1 CS 1— I 


?t7 

CO CO CO 


14-6 

15-10 

14-10 


1 

a 

a 

o 
U 


c 
o 
S5 
c 

J5 


»-H T— ( 

,-H CS 1— 1 

1 1 1 

r^ oor^ 


0\ ON ON 


o ^ o 

»— t 1— 1 1-H 


^ vo Q 

»— 1 1— 1 1— 1 


1-H lO CO 

1 t 1 

CO CO CO 


13-10 

14-6 

14-2 


tiO 

CJ 

»-i 

> 
< 


1—1 1-H 

T-H CS ^ 

1 1 1 

t^ oor^ 


1— 1 oo vo 

1 1 1 

ON On ON 


»-c CS OO 

r— ( 1-H .-H 


i-»CSCN 

»-H »-H ^H 


1 1 1 
CO CO CO 


14-2 

14-11 

14-7 




8-0 

7-10 

8-0 


CO CN CS 

1 1 1 
ON ON ON 


10-11 
10-11 
10-11 


cs cs cs 

>-H »-H 1— ( 


7tt 
CO CO CO 

1-H 1-H »-H 


3n 

1-H 1—1 1-H 


13 

4-1 

c 


7-10 
7-11 
7-10 


T+l W-> T+l 

ON o\ cK 


vo oo oo 

1-H r-( 1-H 


11-9 
12-0 

11-11 


1— 1 1— ( 1-H 
1 1 1 

CO CO CO 

»-H 1— ( 1-H 


■^ ^^ ^^ 

T-H 1-H 1-H 




Rural 
Cities 
General 


Rural 
Cities 
General 


Rural 
Cities 
General 


Rural 
Cities 
General 


Rural 
Cities 
General 


Rural 
Cities 
General 




X! 








> 


> 


1— I 
> 


1— 1 
> 


\—\ 
>—< 

> 



66 



TABLE XIX. 



MEDIAN SCORES FOR A CITY EXPRESSED AS DEVIATIONS FROM 
THE GRADE NORMS 



! 


Ages 


Quotients 




M.A. 


Arith. 


Aver. 


Reading 


I.Q. 


Arith. 


Aver. 


Reading 




Comp 


Rate 


Comp 


Rate 


Ill 

IV 

V 

VI 

VII 

VIII 


—1 


—2 

±i 

+4 


—2 
—3 
—6 
—9 
—1 
+2 


—1 


—2 
—1 

+4 
+ 1 


+4 
—1 
—3 
+ 8 
+ 10 
+8 


—6 



—7 
—1 

—7 


+2 
+2 
+2 
+6 




—6 
—1 

—5 
—7 
+ 1 

+5 


—1 

—2 
+4 
—1 
—2 
—1 


+2 
+2 
+4 
—1 

+ 1 


+0 
—4 
+5 
—2 
—3 
—3 



The intelligence quotients derived from the Illinois General In- 
telligence Scale exhibit a greater degree of variability than those derived 
from the Binet Scale for Measuring Intelligence. For this reason one 
must use a different basis for interpreting the I. Q. 's in terms of degrees of 
brightness. Intelligence quotients derived from the Illinois General 
Intelligence Scale are estimated to be distributed as shown below* The 
appropriate interpretation is indicated in the left-hand column. 

Degree of brightness I.Q. Percent of all 

children included 

"Near" genius or genius 140 and above 1 

Very superior 125-139 6 

Superior 115-124 13 

Normal or average 85-1 14 60 

Dull.... 75-84 13 

Border-line 60-74 6 

Feeble-minded Below 60 1 

Achievement quotients exhibit a somewhat greater degree of variability 
than intelligence quotients. Their distribution differs from the normal by 
showing a greater degree of variability above the median (approximately 
100) than below the median. It is, however, possible to divide the dis- 
tribution so that the percent of pupils included in each division corresponds 
to that used for the interpretation of intelligence quotients. The follow- 
ing scheme for interpretation is suggested: 



*It is necessary to estimate this distribution because the original rule for translating 
point scores into mental ages was found to be unsatisfactory. 



^1 



Quality of pupils' achievement Achievement Percent of 

Quotient pupils included 

Very superior 165 and above 1 

135-164 6 

Superior 117-134 13 

Average 83-116 60 

Poor....; 71-82 13 

55-70 6 

Failure Below 55 1 

Equivalence of Form 1 and Form 2. In considering norms for the 
two forms of the Illinois Examination it is necessary to inquire concerning 
the equivalence of the two forms. In case one form is easier than the other 
the same norms cannot be used. Data with reference to the equivalence 
of the scales which make up the Illinois Examination have already been 
given (See pages 9-18). These facts may be summarized and expressed in 
the following form which is more convenient to use. In order to reduce 
Form 2 age scores to the equivalence of Form 1 scores multiply by the 
following correction numbers: 

Correction 
Number 

Illinois General Intelligence Scale .98 

Monroe's General Survey Scale in Arithmetic, Scale I. .96 
Monroe's General Survey Scale in Arithmetic, Scale II 1 .00 
Monroe's Standardized Silent Reading Test I, Re- 
vised, Comprehension 1 .00 

Rate 1.05 

Monroe's Standardized Silent Reading Test II, Re- 
vised, Comprehension .99 

Rate 97 

Practise effect when a test is repeated. The grade norms given in 
Table XVIII are for the first application of the Illinois Examination. 
When it is given a second time pupils will tend to make higher scores be- 
cause of their acquaintance with the nature of the tests. The amount 
of increase varies. If pupils are "coached" upon the tests a large increase 
is to be expected. When a period of several months intervenes between 
the first and second trials and the pupils have received no training upon the 
exercises of the tests, the increase appears to be small and in some cases 
can be neglected without serious error. No evidence was obtained relative 
to the effect of using the same form instead of a different form. 



6^ 



In order to ascertain the effect of practise when the second appHca" 
tion immediately follows the first, both Form 1 and Form 2 were given to a 
number of pupils. Due to a miscarriage of plans the practise effect for 
the silent reading tests was not determined. For the Illinois General In- 
telligence Scale the average practise effect is approximately 5.0 points, 
or six months of mental age, if the returns from the eighth grade pupils 
are not used. In this grade unusual conditions appear to have prevailed 
and when the scores from it are included the practice effect is approxi- 
mately 7.0 points. For Monroe's General Survey Scale in Arithmetic 
the average practise effect is approximately 3.2 points in grades III to V 
and 4.5 points in grades VI to VIII. It is, therefore, obvious that when the 
Illinois Examination is repeated after only a short interval the second 
trial scores must be corrected before they can be compared with those 
obtained from the first trial. 

In one school the teachers of 134 pupils gave special drill and instruc- 
tion to their pupils after Form 1 of the Illinois Examination had been given 
in November. The teachers did not know that Form 2 was to be given 
later, and did not have in mind, therefore, preparing the pupils for it. 
Their instruction was, to a slight extent, based upon Form 1 test papers. 
Believing that their pupils were rather weak in knowledge of vocabulary 
and in synonym-antonym, special drill was given along these lines in lan- 
guage work. In arithmetic practise was given upon those combinations 
where the pupils seemed weak. In reading there was some special drill 
for increasing the rate of silent reading. The gains made by the pupils 
under these teachers are given in Table XX. 

It is commonly assumed that general intelligence is unaffected by 
school instruction. A median gain of 43.2 points or slightly more than 
four years in mental age within a period of six months indicates that 
mental age, as measured by such an instrument as the Illinois Intelligence 
Scale, is affected by class room instruction. It is, therefore, necessary to 
exercise a great deal of caution in interpreting changes in the intelligence 
scores derived from two successive testings separated by a considerable 
time interval. Even in the case of a first trial the scores obtained will be 
misleading if the pupils have received any special preparation for the test. 

One would naturally expect that the achievement scores in arithme- 
tic and silent reading would be materially affected by instruction. Table 
XX shows very large gains in achievement. The increases in achieve- 
ment quotients show that except for the comprehension of silent reading 
the gains are relatively larger in achievement than in mental age. It is 
not unlikely that some of the increases in the May scores over the Novem- 
ber scores are due to the pupils being more familiar with the testing pro- 
cedure. The effect of familiaritv was not investigated but due caution 

69 



TABLE XX. 



GAINS DUE TO SPECIAL INSTRUCTION UPON THE ILLINOIS 

EXAMINATION 





Median Point Scores 


Median Quotients 




Nov. 
1920 


May 
1921 


Gain 


Nov. 
1920 


May 
1921 


Gain 


Intelligence 

Arithmetic 

Comprehension.. 
Rate 


57.6 

48.2 

10.9 

171.4 


100.8 

120.0 

15.5 

237.9 


43.2 

71.8 

4.6 

66.5 


99.6 
114.0 
105.1 
122.0 


128.0 

137.4 
102.0 
1.39.4 


28.4 

23.4 

—3.1 

17.4 







should be exercised in interpreting the gains in achievement as being the 
result of instruction directed to the needs of the pupils. 



70 



LIBRARY OF CONGRESS 



III III! I III III II III II 

019 842 545 P 




BULLETINS OF THE BUREAU OF EDUCATIONAL RESEARCH, 
COLLEGE OF EDUCATION, UNIVERSITY OF 
ILLINOIS, URBANA, ILLINOIS 

Price 
No. I. Buckingham, B. R. Bureau of Educational Research, An- 
nouncement, 1918-19 15 

No. 2. First Annual Report 25 

No. 3. Bamesberger, Velda C. Standard Requirements for Mem- 
orizing Literary Material 50 

No. 4. Holley, Charles E. Mental Tests for School Use. (Out 

of print) 50 

No. 5. Monroe, Walter S. Report of Division of Educational 

Tests for 1919-20 25 

No. 6. Monroe, Walter S. The Illinois Examination 50 

No. 7. Monroe, Walter S. Types of Learning Required of Pupils 

in the Seventh and Eighth Grades and in the High School .15 

No. 8. Monroe, Walter S. A Critical Study of Silent Reading Tests. 

(In preparation) 50 



